Suppose that $16,065 is invested at an interest rate of 6.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years?5 years? 10 years? c) What is the doubling time?
Answers
Okay, here we have this:
Considering the provided information we obtain the following:
a)
Replacing in the Compound Interest formula we obtain the following:
[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]b)
After 1 year (t=1):
[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]We obtain that after one year the balance is aproximately $17,161.06.
After 2 years (t=2):
[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]We obtain that after two years the balance is aproximately $18,331.90
After 5 years (t=5):
[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]We obtain that after five years the balance is aproximately $22,345.90.
After 10 years (t=10):
[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]We obtain that after ten years the balance is aproximately $31,082.44.
c)
In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:
[tex]32130=16065e^{0.066t}[/tex]Let's solve for t:
[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.
Related Questions
Rachel is driving to Denver. Let y represent her distance from Denver (in miles). Let x represent the time she has been driving (in hours). Suppose that x and yare related by the equation y = 475 - 60x.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.-Picture includes the questions-
Answers
Given the equation:
[tex]y=475-60x[/tex]Let y = distance
Let x = time
- The distance from Denver when she began is given by x = 0, therefore:
[tex]y=475-60(0)=475-0=475[/tex]Answer 1. 475 miles
- The change for each four hours, this is x = 4, so:
[tex]y=475-60(4)=475-240=235[/tex]Answer 2. 235 miles
determine values of the variables that will make the following equation true, if possible. if not, state “not possible”
Answers
Given:
[tex]4\begin{bmatrix}{-r} & & {} \\ {-s} & {} & {} \\ & {} & {}\end{bmatrix}-\begin{bmatrix}{-2r} & & \\ {-2s} & {} & \\ {-2t} & {} & {}\end{bmatrix}=\begin{bmatrix}{-3} & & \\ {-1} & {} & {} \\ {5} & & {}\end{bmatrix}[/tex]As the first matrix has 2 rows and 1 column. And the second matrix has 3 rows and 1 column.
The dimension of both the matrix is not the same.
For the subtraction of two matrices must have the same size.
So, we can not determine the values of variables.
Answer: not possible.
Suppose you are looking to purchase some cans to use for food storage. The can you are looking at has a diameter of 5in. and a height of 7in. What is the volume of the can? Round to the nearest hundredth
Answers
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We are given the diameter is 5
r = d/2 = 5/2 = 2.5 in
V = pi ( 2.5)^2 (7)
V =pi ( 6.25)*7
V = 43.75 pi
Assuming a value for pi of 3.14
V =137.375 in ^3
Rounding to the nearest hundredth
V = 137.38 in ^3
Assuming a value for pi by using the pi button
V = 137.44468
Rounding to the nearest hundredth
V = 137.44 in ^3
What is 16m + 24n? (P.S, this is about factoring expressions.)
Answers
aWe can factorize by a common factor
[tex]16m+24n[/tex][tex](8\times2)m+(8\times3)n[/tex][tex]8(2m+3n)[/tex]ANSWER
8(2m+3n)
What is the y-intercept of f(x) =(3/5)^x?
Answers
Answer:
the y intercept is -1.
Step-by-step explanation:
the y intercept is -1 because it goes through the point (0,-1)
1 + c + 1.4 = c + 2.4I need help
Answers
1 + c + 1.4 = c + 2.4
c + 2.4 = c + 2.4
c = c + 2.4 - 24
c = c
2. Two of your classmates are arguing over the solution to a problem. Rhonda believes that the only method to solving the following theequation below is by using the quadratic equation. Max believes that you can use the quadratic formula but you can also factor theequation. Explain if Rhonda or Max is correct.2x^2-5x=88Some words/phrases to consider using in your response would be:factorFOIL MethodZero-Product PropertyStandard Formquadratic expressionquadratic equationscoefficientperfect square
Answers
Given data:
The given expression is x^2 -6x-7=0.
The given expression can be written as,
[tex]\begin{gathered} x^2-6x=7 \\ x^2-6x+(\frac{6}{2})^2=7+(\frac{6}{2})^2 \\ x^2-2(x)(3)+3^2=7+3^2 \\ (x-3)^2=16 \end{gathered}[/tex]Thus, the number 9 is added on both sides to complete square.
AnimalPossible Locations Relativeto Ocean's Surface25. Reasoning Suppose you plot the locations ofthe animals on a number line. Which animalwould be represented by the point farthest fromO on the number line? Explain. MP2Bloodbelly comb jellyDeep sea anglerfish-0.8 km- km- 2 kmFanfin anglerfishGulper eel-1.1 km26. Which animal is closest to a depth of -0.7 km?Pacific blackdragon- šo kmSlender snipe eel-0.6 km
Answers
Number line
[tex]\ldots-5<-4<-3<-2<\text{ -1< 0<1<2<3<4<5}\ldots[/tex]Let's
[tex]undefined[/tex]for the polyhedron, find the missing numberneed a whole number of faces
Answers
The Euler's polyhedron formula states that, for a polyhedron with F faces, E edges and V vertices, we have:
F + V - E = 2
For E = 12 and V = 6, then we have:
F + 6 - 12 = 2
F = 2 + 12 - 6
F = 8
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 143 subjects with positive test results, there are 24
false positive results; among 150 negative results, there are 5 false negative results. If one of the test subjects is randomly selected, find the probability that the subject
tested negative or did not use marijuana. (Hint: Construct a table.)
The probability that a randomly selected subject tested negative or did not use marijuana is.
(Do not round until the final answer. Then round to three decimal places as needed.)
Answers
The probability that the subject tested negative or did not use marijuana is 145/293.
What is probability?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
As given in the question,
Total positive results are 143 out of which 24 are false, and
total negative results are 150 out of which 5 are false.
We know that,
probability = favorable outcome/ Total outcome
so,
Total outcome = total tests
total tests = 143 + 150
total outcome = 293
and favorable outcome = true negative outcome
true negative outcome = total negative outcome - false negative outcome
true negative outcome = 150 - 5
favorable outcome = 145
Therefore, the probability is equal to 143/293
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help meeeeeeeeee pleaseee !!!!!
Answers
The function 2x + 3x^2 represents the result of adding the two provided functions, f(x) and g(x).
Composite performance.An operation known as "function composition" takes two functions, f and g, and produces a new function, h, that is equal to both g and f and has the property that h(x) = g.
Given the f(x) = 2x and g(x) = 3x^2 functions
The sum of the two functions must be calculated as illustrated;
f(x) + g = (f+g)(x)
Put the provided functions in place of (f+g)(x) to have:
(f+g)(x) = 2x + 3x^2
Standard version of the expression is (f+g)(x) = 2x + 3x^2
Consequently, the sum of the functions f(x) and g(x) is2x + 3x^2
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An item is regularly priced at $65. Lena bought it on sale for 60% off the regular price. How much did Lena pay?
Answers
The regular price of an item is $65
Lena bought it on sale for 60% off the regular price.
Then it means that she paid only (100% - 60% = 40%) of the price.
Let us find the 40% of $65
[tex]\frac{40}{100}\times\$65=\$26[/tex]Therefore, Lena paid only $26 for the item.
In the figure below, m∠1 = 8x and m∠2 = (x-9). Find the angle measures.
Answers
Answer:
• m∠1 =168 degrees
,• m∠2 =12 degrees
Explanation:
From the diagram, Angles 1 and 2 are on a straight line.
We know that the sum of angles on a straight line is 180 degrees.
Therefore:
[tex]m\angle1+m\angle2=180^0[/tex]Substituting the given values, we have:
[tex]\begin{gathered} 8x+x-9=180^0 \\ 9x=180+9 \\ 9x=189 \\ x=\frac{189}{9} \\ x=21 \end{gathered}[/tex]The measures of angles 1 and 2 are:
[tex]\begin{gathered} m\angle1=8x=8\times21=168^0 \\ m\angle2=x-9=21-9=12^0 \end{gathered}[/tex]The measures of angles 1 and 2 are 168 degrees and 12 degrees respectively.
If the calculator gives us the following values number 7
Answers
we know that
The equation is of the form
y=ax+b
The given values are
a=0.872
b=25.263
substitute
therefore
The equation is
y=0.872x+25.263Systems of 2 Equations Word Problems
Answers
Let x and y be the two numbers
x + y = 72 ------------------------------(1)
x - y = 4 ----------------------------------(2)
Add equation (1) and equation (2)
2x = 76
Divide both-side of the equation by 2
x = 38
substitute x = 38 into equation (1) and then solve for y
38 + y = 72
subtract 38 from both-side of the equation
y = 72 - 38
y = 34
The two numbers are 34 and 38
what is the geometric sequence of 2 4
Answers
an = ar^ (n- 1)
for n = 3 (3rd term)
r = common ratio = 4/ 2 = 2
a3 = 2 (2) ^ (3-1)
a3 = 2 (2)^2
a3 = 2 (4)
a3 = 8
n= 4 (4th term)
a4 = 2 (2)^(4-1)
a4 = 2 (2)^3
a4 = 2 (8)
a4 = 16
2, 4 , 8 , 16
452 pointsTo factor x2 + bx + c, the numbers you choose to fill in the empty spots of (x + )(x + ).1mustchoose your answer...to equal c.2Previous34Сл
Answers
The Quadratic format is
[tex]\begin{gathered} x^2\text{ + bx + c } \\ \text{The b is gotten by adding the factors } \\ \text{But the c is gotten by multiplying the factors } \end{gathered}[/tex]The answer to the question is that the factors must multiply to form c
Study the diagram, where AB and C'D are chords that intersect inside of the circle at point P, which is not the center.
Answers
Answer:
answer of the given question
Given the matrices A and B shown below, find 4B – į A.3A=( 1215B5
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Step 1 : To determine the matrices as shown below
Math for Liberal Arts Lecture Class, Fall 2021 = Homework: Ch... Question 2, 1.1.3 Part 2 of 3 HW Score: Points: An election is held to choose the chair of a department at a university. The candidates are Professors Arg for short). The following table gives the preference schedule for the election. Use the table to complete pa Number of Voters 7 9 2 5 3 6 1st choice А A B D A 2nd choice B D D А E E 3rd choice D B E C B B 4th choice E C A B C D 5th choice C E C D A C (a) How many people voted in this election? ... 32 voters (Type a whole number.) (b) How many first-place votes are needed for a majority?
Answers
a) In this election voted: 7+9+2+5+3+6=32
b) For a majority you can follow the next rule:
The 50% of 32 is: 32*0.5=16, then, are needed at least 17 votes
c) Candidate A had 3 last-place votes, candidate B had 0 last-place votes, candidate C had 15 last-place votes, candidate D had 5 last-place votes and candidate E had 9 last-place votes.
Thus, the candidate with the fewest last-place votes is candidate B
Find the number that belongsin the green box.[?]109°13°6Round your answer to the nearest tenth.
Answers
step 1
Find the measure of the third interior angle of triangle
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
x+109+13=180
solve for x
x=180-122
x=58 degrees
step 2
Applying the law of sines
?/sin(13)=6/sin(58)
solve for ?
?=(6/sin(58))*sin(13)
?=1.6 unitsAngela bought a calculator on sale for 15% off. Sales tax is 7.5%. If the calculator cost x dollars, which expression represents the total cost of the calculator?A). (x-0.15) (0.075)B). (x-0.15) (1.075)C). (x-0.15x) (0.075)D). (x- .015x) (1.075)
Answers
Original price = x
Price with 15% off = x - 0.15x
Price with 15% off and 7.5% tax = (x - 0.15x)(1.075)
Answer:
Option B: (x - 0.15x)(1.075)
In TUV, the measure of V=90°, the measure of U=58°, and TU = 38 feet. Find the length of VT to the nearest tenth of a foot.
Answers
Answer:
32.2 feet
Explanation:
The diagram given is a right angled triangle
Using the SOH CAH TOA identity
Given the following
Hypotenuse = 38
Opposite = x
Sin theta = opposite/hypotenuse
Sin 58 = x/38
x = 38sin58
x = 38(0.8480)
x = 32.23
Hence the length of VT to the nearest tenth of a foot. is 32.2feet
Mrs. Laurence just bought a new car for 26,304. She plans to pay her car off in 24 months. Mr. Gannon just bought a new car for 20,480 and plans to pay his car off in 20 months. How much more money a month does Mrs. Laurence pay in her car payment?
Answers
The amount of extra money a month that Mrs. Laurence pays in her car payment is $72.
How much more money does Mrs. Laurence pay each month?We can get the amount of extra amount that Mrs. Laurence pays each month when compared to Mr. Gannon by dividing the amount that they pay by the number of months they need to make these payments.
This can be done as follows:
26304 ÷ 24 = 1096
20480 ÷ 20 = 1024
1096 - 1024 - 72
So, the amount of extra money that Mrs. Laurence has to pay each month when compared to that of Mr. Gannon is $72.
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At an all-you-can-eat barbeque fundraiser, adults pay $6 for a dinner and children pay $4 for a dinner. 212 people attend and you raise $1,128. What is the total number of adults and the total number of children attending? A)140 adults and 72 children B)72 adults and 140 children C)142 adults and 70 children D)70 adults and 142 children
Answers
A)140 adults and 72 children
Explanation
Step 1
Let x represents the number of childrend attending
Let y represents the number of adults attending
then
total cost for the children=4x
total cost for the adults=6y
if you raise 1128,
[tex]4x+6y=1128\text{ Equation(1)}[/tex]Now, 212 people attend,Hence
[tex]x+y=\text{212 Equation(2)}[/tex]Step 2
solve for x and y
a)isolate x in equation (2), then replace in equation (1)
[tex]\begin{gathered} x+y=212 \\ x=212-y \\ \text{now, replace} \\ 4x+6y=1128 \\ 4(212-y)+6y=1128 \\ 848-4y+6y=1128 \\ 2y+848=1128 \\ \text{subtract 848 in both sides} \\ 2y+848-848=1128-848 \\ 2y=280 \\ d\text{ivide boths ides by 2} \\ \frac{2y}{2}=\frac{280}{2} \\ y=140 \end{gathered}[/tex]it means 140 adults are attending
b)replace y=140 in equatin (2) to find x
[tex]\begin{gathered} x+y=212 \\ x+140=212 \\ \text{subtract 140 in both sides} \\ x+140-140=212-140 \\ x=72 \end{gathered}[/tex]so, the number of children is 72 and 72 children
If 340 grams of a substance are present initially and 50 years later only 170 grams remain, how much of the substance will be present after 120 years?Round to the nearest tenth of a graim.grams
Answers
Given -
Substance present initially = 340 grams
Substance present 50 years later = 170 grams
To Find -
How much of the substance will be present after 120 years =?
Step-by-Step Explanation -
Since the substance was reduced to half of what it is initially in 50 years.
So,
The half-life time of the substance = 50 Years.
It means that every 50 years, the substance will reduce to half of its quantity.
And, we know the formula:
[tex]\text{ A = S\lparen}\frac{1}{2}\text{\rparen}^{\frac{t}{h}}[/tex]Where,
A = the remaining amount of Substance =?
S = the amount of Substance you start with = 340grams
t = the amount of time in years = 120 years
h = the half-life time = 50 years
Simply putting the values, we get:
[tex]\begin{gathered} A\text{ = 340}\times(\frac{1}{2})^{\frac{120}{50}} \\ \\ A\text{ = 17\lparen}\frac{1}{2}\text{\rparen}^{2.4} \\ \\ A\text{ = 17}\times(0.5)^{2.4} \\ \\ A\text{ = 17}\times0.1894 \\ \\ A\text{ = 3.22 gram} \end{gathered}[/tex]Final Answer -
The substance that will remain after 120 years = 3.22 gram
Find any domain restrictions on the given rational equation:
X+2
-25
+1=
8x
2x-10
Select all that apply.
A. x = 5
127
B. x = -2
C. X = -5
D. x = 0
Answers
The domain restrictions on the rational equation
[tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are Options A and C. x = 5 and x = - 5 .
What are domain restrictions?A domain restriction is a prescription or criterion that limits the range of possible values for a function. A domain in mathematics is the collection of all values for which a function produces a result. Domain constraints allow us to create functions defined over numbers that meet our needs.Functions defined in pieces are made up of various functions with distinct domain restrictions. Some functions are not allowed to accept values that would make them undefined.How to find the domain restrictions?
The numbers that makes the denominators zero and the entire expression infinite or undefined are the domain restrictions.
Consider the denominators,
[tex]x^{2}[/tex] - 25 ≠ 0 --(1)
[tex]x^{2}[/tex] ≠ 25
x ≠ 5 and x ≠ -5
2x - 10 ≠ 0 ---(2)
2x ≠ 10
x ≠ 10/2
x ≠ 5
The domain restrictions on the rational equation [tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are
x ≠ 5 and x ≠ -5 .
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Can you help me answer part A and part B?
Answers
Part A.
Given:
P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)
Let's find the component of the vector PQ + 5RS.
To find the component of the vector, we have:
[tex]=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>[/tex]For vector RS, we have:
[tex]=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>[/tex]Hence, to find the vector PQ+5RS, we have:
[tex]\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}[/tex]Therefoee, the component of the vector PQ+5RS is:
<-18, -26>
• Part B.
Let's find the magnitude of the vector PQ+5RS.
To find the magnitude, apply the formula:
[tex]m=\sqrt{\left(x^2+y^2\right?}[/tex]Thus, we have:
[tex]\begin{gathered} m=\sqrt{\left(-18^2+-26^2\right?} \\ \\ m=\sqrt{324+676} \\ \\ m=\sqrt{1000} \\ \\ m=\sqrt{10\ast10^2} \\ \\ m=10\sqrt{10} \end{gathered}[/tex]Therefore, the magnitude of the vector is:
[tex]10\sqrt{10}[/tex]ANSWER:
Part A. <-18, -26>
Part B. 10√10
Solve. 0.25(60) + 0.10x = 0.15(60+x)
Answers
[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]
ATTACHED IS THE SOLUTION
Find the surface area of a right cone that has a radius of 9 inches and a height of 12 inches. Round your answer to the nearest hundredth. The surface area is about ⬜ square inches.
Answers
The surface area of the right cone is:
[tex]678.58in^2[/tex]Explanation:The surface area of a right cone is:
[tex]A=\pi r(r+\sqrt[]{r^2+h^2})[/tex]Here, r = 9 in, and h = 12 in
so
[tex]\begin{gathered} A=9\pi(9+\sqrt[]{9^2+12^2}) \\ \\ =9\pi(9+15) \\ =216\pi \\ =678.58in^2 \end{gathered}[/tex]