Question 1

The population P of a culture of bacteria is described by the equation  , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at t = 3 hours? After how many hours will the population reach 7000? Round to the nearest tenth of an hour.

Accepted Answer

The answer of The population P of a culture of...

Question 2

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution. What is [H⁺] if the

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The answer of The chemical acidity of a solution is...

Question 3

The population P of a bacteria culture is modeled by  , where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

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The answer of The population P of a bacteria culture...

Question 4

An investment is expected to pay 5% per year compounded continuously. If you want the value of the investment to be $900,000 after 25 years, how much should you invest initially? Round to the nearest dollar.

Accepted Answer

We can use the formula for continuous compounding:

$A = Pe^{rt}$

where A is the final amount, P is the initial investment, r is the annual interest rate (in decimal form), and t is the time period.

Plugging in the given values, we get:

$900,000 = Pe^{0.05 \cdot 25}$

Solving for P, we get:

$P = \dfrac{900,000}{e^{1.25}} \approx \$257,854$

Rounding to the nearest dollar, we get the answer of $\boxed{	extbf{(C)}\ 257,854}$.

Question 5

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution. What is the pH if ? Round to the nearest hundredth.

Accepted Answer

The answer of The chemical acidity of a solution is...

Question 6

Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is ¹⁴C is constant. The amount of ¹⁴C in an object made from harvested plants, like paper, will decline exponentially according to the equation , where A represents the amount of ¹⁴C in the object, A_o represents the amount of ¹⁴C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 25% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year.

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The answer of Carbon dating presumes that, as long as...

Question 7

The value of an investment is presently $9186.79. It had been paying 8% compounded continuously since the investment was made 10 years ago. How much was invested originally?

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Question 8

An initial investment of $5000 doubles in value in 11 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Accepted Answer

Using the formula for continuous compounding:

A = Pe^(rt)

Where:

A = final amount = $10,000
P = initial amount = $5000
r = interest rate
t = time in years = 11

Substituting the known values:

$10,000 = $5000e^(11r)

Dividing by $5000:

2 = e^(11r)

Taking the natural logarithm of both sides:

ln(2) = 11r

Solving for r:

r = ln(2)/11 ≈ 0.0633

Converting to a percentage and rounding to the nearest tenth:

r ≈ 6.3%

Therefore, the answer is (D) 6.3%.

Quiz 8: Exponential and Logarithmic Functions

The population P of a culture of bacteria is described by the equation , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at t = 3 hours? After how many hours will the population reach 7000? Round to the nearest tenth of an hour.

The chemical acidity of a solution is measured in units of pH: , where [H+] is the hydrogen ion concentration in the solution. What is [H+] if the

The population P of a bacteria culture is modeled by , where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

An investment is expected to pay 5% per year compounded continuously. If you want the value of the investment to be $900,000 after 25 years, how much should you invest initially? Round to the nearest dollar.

The chemical acidity of a solution is measured in units of pH: , where [H+] is the hydrogen ion concentration in the solution. What is the pH if ? Round to the nearest hundredth.

The value of an investment is presently $9186.79. It had been paying 8% compounded continuously since the investment was made 10 years ago. How much was invested originally?

An initial investment of $5000 doubles in value in 11 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution. What is [H⁺] if the

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution. What is the pH if ? Round to the nearest hundredth.