Question:
There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal is poured into the bowl at a rate of 1.5 ounces per second. How many ounces are in the bowl after 3 seconds?
Solution:
If additional cereal is poured into the bowl at a rate of 1.5 ounces per second, then in 3 seconds the additional cereal into the bowl is 1.5x 3 = 4.5 ounces. Thus after 3 seconds, the bowl has the original amount that it already had and the new aggregate:
9.75 ounces + 4.5 ounces = 14.25
then, the correct answer is:
14.25
What is 5,435,778 expressed in scientific notation?A.5.435778 x 10*7B.5.435778 x 10*3C.5.435778 x 10*6D.5.435778 x 10*5
Given the number
[tex]5,435,778[/tex]We can express it in scientific notation below;
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
Therefore, in the given question, we will have;
[tex]5,435,778=5.435778\times10^6[/tex]Answer: Option C
I need help finding 5 points. the vertex, 2 to the left of the vertex, and 2 points to the right of the vertex.
Let's convert the given equation first into a vertex form.
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the vertex.
The vertex form of the equatio that we have is:
[tex]y=-2(x-0)^2+0[/tex]Hence, the vertex of the equation is at the origin (0, 0).
Since "a" is negative, our parabola is opening downward.
Let's identify two points to the left of the vertex. Let's say at x = -1. Replace "x" with -1 in the equation.
[tex]\begin{gathered} y=-2(-1)^2 \\ y=-2(1) \\ y=-2 \end{gathered}[/tex]Hence, we have a point to the left of the parabola at (-1, -2).
Let's say x = -2. Replace "x" with -2 in the equation.
[tex]\begin{gathered} y=-2(-2)^2 \\ y=-2(4) \\ y=-8 \end{gathered}[/tex]Hence, we also have another point to the left of the parabola at (-2, -8).
If our x is to the right of the vertex, say, x = 1. Replace "x" with 1 in the equation.
[tex]\begin{gathered} y=-2(1)^2 \\ y=-2(1) \\ y=-2 \end{gathered}[/tex]We have a point to the right of the parabola at (1, -2).
If x = 2, let's replace "x" with 2 in the equation.
[tex]\begin{gathered} y=-2(2)^2 \\ y=-2(4) \\ y=-8 \end{gathered}[/tex]Hence, we also have another point to the right of the parabola at (2, -8).
The graph of this equation is:
Slope of Linear EquationsWhich description best compares the graph given by the following equations:23-5y = 82Y == -6Choose one. 4 pointsO parallelO perpendicularintersecting but not perpendicularO coinciding
Answer:
The two lines are parallel.
Explanation:
We have the equations:
[tex]\begin{gathered} 2x-5y=8 \\ y=\frac{2}{5}x-6 \end{gathered}[/tex]Let's solve the first one for y, so we get the same formatting on both euqations:
[tex]\begin{gathered} 2x-5y=8 \\ 5y=2x-8 \\ y=\frac{2}{5}x-\frac{8}{5} \end{gathered}[/tex]SInce the two lines have the same slope, 2/5, the two lines are parallel.
I don't understand please explain in simple words the transformation that is happeningwhat is the function notation
We have the next functions
[tex]f(x)=5^x^{}[/tex][tex]g(x)=2(5)^x+1[/tex]Function notation
[tex]g(x)=2(f(x))+1[/tex]Describe the transformation in words
we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit
Find the volume of this triangular prism.Be sure to include the correct unit in your answer.8 cm7 cm→5 cm
The formula to find the volume of a triangular prism is the following:
[tex]V=\frac{1}{2}h\cdot b\cdot w[/tex]where:
h - height
b - base length
w - width
for this problem:
h = 8 cm
b = 5 cm
w = 7 cm
then
[tex]V=\frac{1}{2}8\cdot5\cdot7[/tex]solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters
The length of a rectangle is 5 ft less than double the width, and the area of the rectangle is 33f * t ^ 2 Find the dimensions of the rectangle. length___with____
The length of rectangle is : 6ft .
Width of rectangle is : 5.5ft .
What is an area of rectangle?The area of rectangle is :
A = l × w
Here given,
length is 5ft less than twice the width,
So the equation can be represented in terms of length as,
l = 2w - 5
Given area = 33sqft
By substituting value of length,
33 = (2w - 5) × w
By applying distributive property,
33 = 2w² - 5w
= 2w² - 5w - 33
By factoring the equation:
(2w - 11)(w + 3) = 0
To find value of zeros,
2w - 11 = 0
2w = 11
w = 5.5
Similarly,
w + 3 = 0
w = -3
Since width cannot be negative , the width will be:
the width = 5.5 ft.
Also find length by substituting value of width in equation,
33 = 5.5l
33/5.5 = l
l = 6 ft.
∴ The length = 6ft, and width = 5.5ft.
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Yesterday, Diane had c baseball cards. Today, she gave 6 away. Using c, write and expression for the number of cards Diane has left.
Answer:
The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.
determine the value of x nodes following quadrilateral
The value of x nodes given quadrilateral is 80° which is determined by the measure of the supplemental interior angle.
What is the quadrilateral?A quadrilateral is a polygon with four sides. This also indicates that a quadrilateral has four vertices and four angles.
Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
First, we have to find the measure of the supplemental interior angle
Here take the exterior angle1 = 100° and exterior angle2 = 60°, find its interior angles
⇒ 100 + int.1 = 180 ⇒ int.1 = 180 - 100 = 80°
⇒ 60 + int.2 = 180 ⇒ int.2 = 180 - 60 = 120°
Since the sum of all interior angles of a polygon = 360°
As per the given figure,
x + 80 + x + 120 = 360
2x = 360 - 200
2x = 160
x = 80°
Therefore, the value of x nodes given quadrilateral is 80°.
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*Statistical question: Is the proportion of inner-city families living on a subsistence income: 20%? Two hundred families were randomly selected for the survey
and 38 were found to have income at the subsistence level. Use the formal critical value method at 5% level of significance.
List the assumptions pertaining to this procedure.
Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.
Hypothesis tested and critical valueAt the null hypothesis, it is tested if the proportion is of 20%, that is:
[tex]H_0: p = 0.2[/tex]
At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:
[tex]H_1: p \neq 0.2[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
Test statisticThe test statistic is given by the rule presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In the context of this problem, the parameters are given as follows:
[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]
z = -0.35.
|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.
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What is the seventy-seven is forty-six more than r
Answer: 77 = 46 + r, r = 31
Step-by-step explanation:
We will write an equation to represent this situation. Then, we will solve for r by isolating the variable.
Seventy-seven is forty-six more than r.
77 is forty-six more than r.
77 = forty-six more than r.
77 = 46 more than r.
77 = 46 + r
77 = 46 + r
(77) - 46 = (46 + r) - 46
31 = r
r = 31
Can someone help me with this math question. I just need to see the work.
pic of question below
The polar coordinates for each point are given as follows:
a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]
b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]
Polar coordinatesSuppose we have a point with Cartesian coordinates given as follows:
(x,y).
The polar coordinates will be found as follows:
r² = x² + y².θ = arctan(y/x).For item a), the Cartesian coordinates are as follows:
(-4, 4).
Hence the polar coordinates will be given as follows:
r² = (-4)² + (4)² -:> r = sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.For item a), the Cartesian coordinates are as follows:
(3, 3sqrt(3)).
Hence the polar coordinates will be given as follows:
r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.More can be learned about polar coordinates at https://brainly.com/question/7009095
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An observer in a lighthouse 350 ft above sea level observes two ships directly offshore. The angles of depression to the shops are 4 degree and 6.5 degree. How far apart are the ships?
The two ships are 1933.32 ft apart
Explanation:Given:
The height of the lighthouse = 350 ft
The angles of depression to the ships are 4 degree and 6.5 degree
To find:
the distance between the two ships
To determine the distance, we will use an illustration of the situation
First we will find the value of y as we need to know this value to get x
To get y, we will apply tan ratio (TOA)
[tex]\begin{gathered} tan\text{ 6.5\degree = }\frac{opposite}{adjacent} \\ opp\text{ = 350 ft} \\ adj\text{ = y} \\ tan\text{ 6.5\degree = }\frac{350}{y} \\ y(tan\text{ 6.5\degree\rparen= 350} \\ y\text{ = }\frac{350}{tan\text{ 6.5}} \\ y\text{ = 3071.9106 ft} \end{gathered}[/tex]Next is to find x using tan ratio (TOA):
[tex]\begin{gathered} angle\text{ = 4\degree} \\ tan\text{ 4\degree= }\frac{opposite}{adjacent} \\ \\ opposite\text{ = 350 ft} \\ adjacent\text{ = y + x} \\ tan\text{ 4\degree= }\frac{350}{y\text{ + x}} \end{gathered}[/tex][tex]\begin{gathered} tan\text{ 4 = }\frac{350}{3071.9106+x} \\ \frac{350}{tan\text{ 4}}\text{ = 3071.9106 + x} \\ 5005.2332\text{ = 3071.9106 + x} \\ x\text{ = 1933.3226} \\ \\ The\text{ ships are 1933.32 ft apart \lparen nearest hundredth\rparen} \end{gathered}[/tex]a circular cylinder with a diameter of 12 cm and a height of 27 cm is filled with water. An aquarium is in the shaoe of a rectangular prism with the dimensions 35 cm 40cm by 42cm. what isvthe maximum number of full cylinders that can be poured into the fish tank without overflowing it?
Given data:
The diameter of cylinder is d=12 cm.
The height of the cylinder is h= 27 cm.
The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).
The volume of the cylinder is,
[tex]\begin{gathered} V^{\prime}=\frac{\pi}{4}(d)^2h \\ =\frac{\pi}{4}(12cm)^2(27\text{ cm)} \\ =3053.628cm^3 \end{gathered}[/tex]The volume of the aquarium is,
[tex]\begin{gathered} V=(35\text{ cm)(40 cm)(42 cm)} \\ =58800cm^3 \end{gathered}[/tex]The number of cylinders that can be pour into aquarium is,
[tex]\begin{gathered} n=\frac{V}{V^{\prime}} \\ =\frac{58800}{3053.628} \\ =19.25 \end{gathered}[/tex]Thus, the number of cylinders that can be pour into aquarium is 19.25.
I need help question 10 b and c
Part b.
In this case, we have the following function:
[tex]y=5(2.4)^x[/tex]First, we need to solve for x. Then, by applying natural logarithm to both sides, we have
[tex]\log y=\log (5(2.4^x))[/tex]By the properties of the logarithm, it yields
[tex]\log y=\log 5+x\log 2.4[/tex]By moving log5 to the left hand side, we have
[tex]\begin{gathered} \log y-\log 5=x\log 2.4 \\ \text{which is equivalent to} \\ \log (\frac{y}{5})=x\log 2.4 \end{gathered}[/tex]By moving log2.4 to the left hand side, we obtain
[tex]\begin{gathered} \frac{\log\frac{y}{5}}{\log2.4}=x \\ or\text{ equivalently,} \\ x=\frac{\log\frac{y}{5}}{\log2.4} \end{gathered}[/tex]Therfore, the answer is
[tex]f^{-1}(y)=\frac{\log\frac{y}{5}}{\log2.4}[/tex]Part C.
In this case, the given function is
[tex]y=\log _{10}(\frac{x}{17})[/tex]and we need to solve x. Then, by raising both side to the power 10, we have
[tex]\begin{gathered} 10^y=10^{\log _{10}(\frac{x}{17})} \\ \text{which gives} \\ 10^y=\frac{x}{17} \end{gathered}[/tex]By moving 17 to the left hand side, we get
[tex]\begin{gathered} 17\times10^y=x \\ or\text{ equivalently,} \\ x=17\times10^y \end{gathered}[/tex]Therefore, the answer is
[tex]f^{-1}(y)=17\times10^y[/tex]Please fill in the blanks so that the following statement is trues
x-intercepts
1) In a quadratic equation, the Real solutions correspond to the points in which the parabola intercepts the x-axis.
2) Note that when the roots are not real solutions, then we'd have complex numbers and the parabola wouldn't intercept the x-axis.
3) Therefore, the answer is: x-intercepts
**Determine the x-value at which the-following function touches but does not cross the x-axis:3x^3- 182 + 27x
Okay, here we have this:
We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.
According with this let's
The variables x and y vary directly. Use values to write an equation that relates x and y. y=25;x=5And y=20;x=12
A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]0.2x + 0.21x - 0.04 = 8.16Solve for "x".
Given the folllowing equation:
[tex]0.2x+0.21x-0.04=8.16[/tex]You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:
[tex]\begin{gathered} 0.2x+0.21x-0.04+(0.04)=8.16+(0.04) \\ 0.2x+0.21x=8.2 \end{gathered}[/tex]2. Now you need to add the like terms on the left side of the equation:
[tex]0.41x=8.2[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:
[tex]\begin{gathered} \frac{0.41x}{0.41}=\frac{8.2}{0.41} \\ \\ x=20 \end{gathered}[/tex]The answer is:
[tex]x=20[/tex]I need these answers quickly. If I don't get them by midnight ill cry.
1. 9c-3c=48A) c=9B) c=3C) c=4D) C=8
To solve this equation, we need to subtract both, 9c - 3c:
[tex]9c\text{ - 3c = 6c = 48}[/tex]Dividing by 6 at both sides of the equation
[tex]\frac{6c}{c}\text{ = }\frac{48}{6}[/tex]Then
[tex]c\text{ = 8}[/tex]Then the answer C = 8. (Option D)
NEED TO FINISH BEFORE 9!!! PLEASE HELP!!!
A rational value that is less than zero is -√4.
An irrational value greater than five is 5 1/9.
A rational value between 10 and 20 is √225.
What are rational numbers and irrational numbers?A rational number is a number that can be expressed as a fraction of two integers. A rational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of rational numbers are 100, -0.5.
A irrational number is a number that cannot be expressed as a fraction of two integers. An irrational number can either be a positive number, negative number, whole number, decimal or fraction. Examples of irrational numbers are 22/7, 1-/9.
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Alejandra categorized her spending for this month into four categories: Rent, Food, Fun, and Other.The percents she spent in each category are pictured here.Food21%Rent30%Other31%Fun18%If Alejandra spent a total of $2500 this month, how much did she spend on Food?
she spent 525 on Food
she spent 750 on rent
she spent 775 on others
she spent 450 on fun
Explanation
to find the value of the percentage of any number just use this formula
[tex]\text{ percentage=}\frac{\text{ x\%}\cdot\text{ Number}}{100}[/tex]so
to find the values, apply the formula
Step 1
a) food :21 %
so
[tex]\begin{gathered} \cos t\text{ of food=}\frac{\text{ 21}\cdot2500}{100} \\ \cos t\text{ of food=}525 \end{gathered}[/tex]it means she spent 525 on Food
Step 2
b) Rent:30 %
so
[tex]\begin{gathered} \cos t\text{ of rent=}\frac{\text{ 30}\cdot2500}{100} \\ \cos t\text{ of rent=}750 \end{gathered}[/tex]it means she spent 750 on rent
Step 3
c)other:31 %
so
[tex]\begin{gathered} \cos t\text{ of other=}\frac{\text{ 31}\cdot2500}{100} \\ \cos t\text{ of other=}775 \end{gathered}[/tex]it means she spent 775 on others
Step 4
d)Fun:18 %
so
[tex]\begin{gathered} \cos t\text{ of fun=}\frac{\text{ 18}\cdot2500}{100} \\ \cos t\text{ of fun=}450 \end{gathered}[/tex]it means she spent 450 on fun
I hope this helps you
Use the change of base formula and a calculator to evaluate the logarithm
The change of base formula states that:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.
In this case we have:
[tex]\begin{gathered} x=14 \\ b=\sqrt[]{3} \end{gathered}[/tex]Then, using the change of base formula, we have:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln 14}{\ln \sqrt[]{3}}[/tex]Once we have the expression we just evaluate the expression on the right to get the appoximation we need:
[tex]\log _{\sqrt[]{3}}14=\frac{\ln14}{\ln\sqrt[]{3}}\approx4.804[/tex]Find the point that partitions segment AB in a 1:3 ratio (_,_)Find the point that partitions segment AD in 1.1 ratio (_,_)
AB in 1:3 ratio, Find a pointwhere on one side there is 1/4 of AB and in the other side 3/4 of AB:
Need help figuring out if the following is Real or Complex Question number 10
Explanation:
We have the expression:
[tex]i^3[/tex]where i represents the complex number i defined as follows:
[tex]i=\sqrt{-1}[/tex]To find if i^3 is real or complex, we represent it as follows:
[tex]i^3=i^2\times i[/tex]And we find the value of i^2 using the definition of i:
[tex]i^2=(\sqrt{-1})^2[/tex]Since the square root and the power of 2 cancel each other
[tex]\imaginaryI^2=-1[/tex]And therefore, using this value for i^2, we can now write i^3 as follows:
[tex]\begin{gathered} \imaginaryI^3=\imaginaryI^2\times\imaginaryI \\ \downarrow \\ \imaginaryI^3=(-1)\times\imaginaryI \end{gathered}[/tex]This simplifies to -i
[tex]\imaginaryI^3=-\imaginaryI^[/tex]Because -i is still a complex number, that means that i^3 is a complex number.
Answer: Complex
How to find the area of a regular hexagon with a radius of 12 inches? Please help
You want to build a sandbox that can hold50,445 cubic inches of sand. If the sandbox is to be59 in. long and57 in. wide, how tall will it need to be?
Volume of sandbox (to be built) = 50,445 cubic inches
A sandbox is the shape of a cuboid and is calculated by the formula
[tex]\text{volume = length }\cdot\text{ wi}\differentialD tth\text{ }\cdot\text{ height }\Rightarrow\text{ v = l }\cdot\text{ w }\cdot\text{ h}[/tex]Volume = Length * Width * Height
Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?
50,445 = 59 * 57 * h
Make h the subject of the formula, we have:
h = 50445 / (59 * 57) = 15 in
using the gcf and the distributive property find the sum of 34+51
it would be 75 ur welcome
SOMEONE PLS HELPPPPPPPP
Answer:
**NEED USEFUL ANSWER ASAP, H.W QUESTION**
Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?
Step-by-step explanation:
11. The population of the District of Columbia was approximately 572 thousand in 2000 and had been growing by about 1.15% per year.(a) Write an explicit formula for the population of DC t years after 2000 (i.e. t=0 in 2000), where Pt is measured in thousands of people.Pt = (b) If this trend continues, what will the district's population be in 2025? Round your answer to the nearest whole number. thousand people(c) When does this model predict DC's population to exceed 800 thousand? Give your answer as a calendar year (ex: 2000).During the year
Given:
Population in 2000 = 572 thousand
Rate of growth per year = 1.15%
Let's solve for the following:
(a) Explicit formula for the population years after 2000.
Where:
In year 2000, t = 0
To write the explicit formula, apply the exponantial growth function formula:
[tex]f(t)=a(1+r)^t[/tex]Where:
a is the initial amount
r is the growth rate.
Thus, we have:
[tex]\begin{gathered} P_t=572(1+\frac{1.15}{100}_{^{}})^t \\ \\ P_t=572(1+0.0115)^t \end{gathered}[/tex]Therefore, the explicit formula for the population years after 2000 is:
[tex]P_t=572(1.0115)^t[/tex](b) What will be the district's population in 2025.
Where:
In the year 2000, t = 0
In the year 2025, t will be = 25
To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:
[tex]\begin{gathered} P_{25}=572(1.0115)^{25} \\ \\ P_{25}=572(1.330905371) \\ \\ P_{25}=761.28\approx761 \end{gathered}[/tex]The population in 2025 if the trend continues will be approximately 761 thousand.
(c) When does the model predict the population to exceeed 800 thousand.
Substitute 800 for Pt and solve for t.
We have:
[tex]\begin{gathered} P_t=572(1.0115)^t \\ \\ 800=572(1.0115)^t \end{gathered}[/tex]Divide both sides by 572:
[tex]\begin{gathered} \frac{800}{572^{}}=\frac{572(1.0115)^t}{572} \\ \\ 1.3986=1.0115^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} \ln (1.3986)=\ln (1.0115)^t \\ \\ \ln (1.3986)=t\ln (1.0115) \\ \\ 0.33547=0.01143t \end{gathered}[/tex]Divide both sides by 0.01143:
[tex]\begin{gathered} \frac{0.33547}{0.01143}=\frac{0.01143t}{0.01143} \\ \\ 29.3=t \\ \\ t=29.3\approx29 \end{gathered}[/tex]When t = 29, the year is 2000 + 29 = 2029
Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.
ANSWERS:
[tex]\begin{gathered} (a)P_t=572(1.0115)^t \\ \\ (b)=761\text{ thousand people} \\ \\ (c)\text{ 20}29 \end{gathered}[/tex]