Question 1

Find the value of x.
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Accepted Answer

The answer of Find the value of x.
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Question 2

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation.
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Accepted Answer

The answer of Fill in the missing coordinate in each...

Question 3

Find the value of x.
- = 1296

Accepted Answer

The answer of Find the value of x.
- = 1296
...

Question 4

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $1000 is appreciated for 7 years in an account that earns 11% interest, compounded annually. Find the amount of money in the account at the end of the period.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt). Here, P = $1000, r = 0.11, n = 1, and t = 7. Plugging in these values, A = 1000(1 + 0.11/1)^(1*7) = 1000(1.11)^7 ≈ $2076.16.

Question 5

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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Question 6

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $1000 is appreciated for 5 years in an account that earns 12% interest, compounded semiannually. Find the amount of money in the account at the end of the period.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Here, P = $1000, r = 12% or 0.12, n = 2 (since the interest is compounded semiannually), and t = 5 years. Plugging these values into the formula gives A = 1000(1 + 0.12/2)^(2*5) = 1000(1 + 0.06)^10 ≈ $1790.85.

Question 7

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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Question 8

Solve the problem.
-The amount of particulate matter left in solution during a filtering process is given by the equation  where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

Accepted Answer

The answer of Solve the problem.
-The amount of particulate matter...

Question 9

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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Question 10

Solve the problem. When needed, use 365 days per year and 30 days per month.
-What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $P$, we get $P = \frac{A}{e^{rt}}$. Given $A = 1190$, $r = 0.08$, and $t = 4$, we find $P = \frac{1190}{e^{0.08 \times 4}}$, which calculates to approximately $864.12.

Question 11

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $480 is appreciated for 9 years in an account that earns 18% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Here, P = $480, r = 18% or 0.18, n = 4 (since the interest is compounded quarterly), and t = 9 years. Plugging these values into the formula gives A = 480(1 + 0.18/4)^(4*9) = $2341.14.

Question 12

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $12,000 is appreciated for 5 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Accepted Answer

The amount of money in the account at the end of the period can be found using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($12,000), r is the annual interest rate (4% or 0.04), n is the number of times that interest is compounded per year (quarterly, so 4 times), and t is the time the money is invested for (5 years). Plugging in the values: A = 12000(1 + 0.04/4)^(4*5) = $14,642.28.

Question 13

Write the equation of the graph in its final position.
-The graph of y =  is translated 9 units to the right, reflected in the y-axis, and then translated 4 units downward.

Accepted Answer

The answer of Write the equation of the graph in...

Question 14

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $480 is appreciated for 8 years in an account that earns 2% interest, compounded continuously. Find the amount of money in the account at the end of the period.

Accepted Answer

The answer of Solve the problem. When needed, use 365...

Question 15

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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Question 16

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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...

Question 17

Write the equation of the graph in its final position.
-The graph of y =  is translated 7 units to the right and then 3 units upward.

Accepted Answer

The answer of Write the equation of the graph in...

Question 18

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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Question 19

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $14,000 is appreciated for 3 years in an account that earns 14% interest, compounded semiannually. Find the amount of money in the account at the end of the period.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where P is the principal amount ($14,000), r is the annual interest rate (0.14), n is the number of times interest is compounded per year (2 for semiannually), and t is the time in years (3). Plugging in these values gives A = 14000(1 + 0.14/2)^(2*3) = 14000(1.07)^6 ≈ $21,010.22.

Question 20

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation.
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Accepted Answer

The answer of Fill in the missing coordinate in each...

Quiz 4: Exponential and Logarithmic Functions

Find the value of x. -

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation. -

Find the value of x. - = 1296

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $1000 is appreciated for 7 years in an account that earns 11% interest, compounded annually. Find the amount of money in the account at the end of the period.

Solve the equation. -

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $1000 is appreciated for 5 years in an account that earns 12% interest, compounded semiannually. Find the amount of money in the account at the end of the period.

Solve the equation. -

Solve the problem. -The amount of particulate matter left in solution during a filtering process is given by the equation where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

Solve the equation. -

Solve the problem. When needed, use 365 days per year and 30 days per month. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $480 is appreciated for 9 years in an account that earns 18% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $12,000 is appreciated for 5 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Write the equation of the graph in its final position. -The graph of y = is translated 9 units to the right, reflected in the y-axis, and then translated 4 units downward.

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $480 is appreciated for 8 years in an account that earns 2% interest, compounded continuously. Find the amount of money in the account at the end of the period.

Solve the equation. -

Solve the equation. -

Write the equation of the graph in its final position. -The graph of y = is translated 7 units to the right and then 3 units upward.

Solve the equation. -

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $14,000 is appreciated for 3 years in an account that earns 14% interest, compounded semiannually. Find the amount of money in the account at the end of the period.

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation. -