Question 1

Simplify the expression.
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Accepted Answer

The answer of Simplify the expression.
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Question 2

Use a graphing calculator to solve the equation. Round to two decimal places.
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Accepted Answer

The answer of Use a graphing calculator to solve the...

Question 3

Simplify the expression.
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Accepted Answer

The answer of Simplify the expression.
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Question 4

Solve the problem.
-If $4000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $9800 at 8%? Round to the nearest tenth.

Accepted Answer

The formula for continuous compounding is $ A = Pe^{rt} $. Here, $ A = 9800 $, $ P = 4000 $, $ r = 0.08 $. Solving for $ t $, we get $ t = \frac{\ln(9800/4000)}{0.08} \approx 11.2 $ years.

Question 5

Solve the problem.
-If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 5.5%? Round to the nearest tenth.

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. To find $t$, we rearrange the formula to solve for $t$: $t = \frac{\ln(A/P)}{r}$. Substituting $A = 5000$, $P = 2500$, and $r = 0.055$, we get $t = \frac{\ln(5000/2500)}{0.055} = \frac{\ln(2)}{0.055}$, which calculates to approximately 12.6 years.

Question 6

Solve the problem.
-If $3000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $9000 at 7%? Round to the nearest tenth.

Accepted Answer

The answer of Solve the problem.
-If $3000 is invested in...

Question 7

Solve the problem.
-The average salary for Major League Baseball players has been increasing exponentially since 1980. The average salary S can be modeled by the exponential equation  where t is the number of years since
1980. Use the model to predict the year when the average salary will be $10 million more than it was in the year
2000?

Accepted Answer

The answer of Solve the problem.
-The average salary for Major...

Question 8

Solve the problem.
-At what interest rate would a deposit of $20,000 grow to $29,836 in 25 years with continuous compounding? Round to the nearest tenth when necessary.

Accepted Answer

The answer of Solve the problem.
-At what interest rate would...

Question 9

Solve the problem.
-If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 8%? Round to the nearest tenth.

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. We are given $A = 5000$, $P = 2500$, and $r = 0.08$. We need to solve for $t$. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Substituting the given values, $t = \frac{\ln(5000/2500)}{0.08} = \frac{\ln(2)}{0.08}$. Calculating this gives $t \approx 8.7$ years.

Question 10

Solve the equation.
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Accepted Answer

The answer of Solve the equation.
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...

Question 11

Solve the problem.
-In 5 years, only 2.7% of the current internet businesses will still be operating. Use the exponential model  to determine the annual rate of internet business failures.

Accepted Answer

The answer of Solve the problem.
-In 5 years, only 2.7%...

Question 12

Solve the problem.
-If $3500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $7900 at 5.5%? Round to the nearest tenth.

Accepted Answer

To solve this, use the formula for continuous compounding: $ A = Pe^{rt} $. Here, $ A = 7900 $, $ P = 3500 $, $ r = 0.055 $. Solving for $ t $, we get $ t = \frac{\ln(\frac{7900}{3500})}{0.055} \approx 14.8 $ years.

Question 13

Simplify the expression.
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Accepted Answer

The answer of Simplify the expression.
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...

Question 14

Use a graphing calculator to solve the equation. Round to two decimal places.
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Accepted Answer

The answer of Use a graphing calculator to solve the...

Question 15

Use a graphing calculator to solve the equation. Round to two decimal places.
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Accepted Answer

The answer of Use a graphing calculator to solve the...

Question 16

Use a graphing calculator to solve the equation. Round to two decimal places.
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Accepted Answer

The answer of Use a graphing calculator to solve the...

Question 17

Solve the problem.
-Ben Franklin bequeathed $4000.00 to the city of Boston in 1790. Assuming the fund grew to $9 million in 200 years, find the interest rate compounded continuously that would yield this total value. Round to the nearest
Tenth when necessary.

Accepted Answer

To find the interest rate compounded continuously, we use the formula A = Pe^(rt), where A is the amount after time t, P is the principal amount, r is the rate, and t is the time in years. Plugging in the values: 9,000,000 = 4,000e^(200r). Solving for r gives approximately 0.039, or 3.9%.

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 equation.
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Accepted Answer

The answer of Solve the equation.
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Question 20

Solve the problem.
-In chemistry, the pH of a substance is defined by  where  is the hydrogen ion concentration in moles per liter. Find the pH of a sample of lake water whose  oles per liter. (Round to the
Nearest tenth.)

Accepted Answer

The answer of Solve the problem.
-In chemistry, the pH of...

Quiz 4: Exponential and Logarithmic Functions

Simplify the expression. -

Use a graphing calculator to solve the equation. Round to two decimal places. -

Simplify the expression. -

Solve the problem. -If $4000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $9800 at 8%? Round to the nearest tenth.

Solve the problem. -If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 5.5%? Round to the nearest tenth.

Solve the problem. -If $3000 is invested in an account that pays interest compounded continuously, how long will it take to grow to $9000 at 7%? Round to the nearest tenth.

Solve the problem. -At what interest rate would a deposit of $20,000 grow to $29,836 in 25 years with continuous compounding? Round to the nearest tenth when necessary.

Solve the problem. -If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 8%? Round to the nearest tenth.

Solve the equation. -

Solve the problem. -In 5 years, only 2.7% of the current internet businesses will still be operating. Use the exponential model to determine the annual rate of internet business failures.

Solve the problem. -If $3500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $7900 at 5.5%? Round to the nearest tenth.

Simplify the expression. -

Use a graphing calculator to solve the equation. Round to two decimal places. -

Use a graphing calculator to solve the equation. Round to two decimal places. -

Use a graphing calculator to solve the equation. Round to two decimal places. -

Solve the problem. -Ben Franklin bequeathed $4000.00 to the city of Boston in 1790. Assuming the fund grew to $9 million in 200 years, find the interest rate compounded continuously that would yield this total value. Round to the nearest Tenth when necessary.

Solve the equation. -

Solve the equation. -

Solve the problem. -In chemistry, the pH of a substance is defined by where is the hydrogen ion concentration in moles per liter. Find the pH of a sample of lake water whose oles per liter. (Round to the Nearest tenth.)