Question 1

A stock analyst attempts to express the price p of a share of XYZ stock as an exponentially increasing function of the time since XYZ's initial public offering (IPO):  , where m is the number of months since the IPO.The price of a share was $10.00 at the time of the IPO and $13.60 four months after the IPO.What is the approximate value of k? Round to the nearest thousandth.

Accepted Answer

The answer of A stock analyst attempts to express the...

Question 2

On the Richter scale, the magnitude  of an earthquake of intensity  per unit of area is given by  where  is the minimum intensity used for comparison.Find the magnitude  (on the Richter scale) of an earthquake of intensity  Round to the nearest thousandth.

Accepted Answer

The answer of On the Richter scale, the magnitude ...

Question 3

Estimate the percentage of radioactive material that remains in a sample after 5 years if the half-life of the material is 299 days.Round to the nearest hundredth of a percent.

Accepted Answer

To solve this problem, we need to use the formula for radioactive decay:

N = N0 * (1/2)^(t/T)

where N is the amount of radioactive material remaining after time t, N0 is the initial amount of radioactive material, T is the half-life, and ^(t/T) represents the number of half-life periods that have passed.

In this case, we know that T = 299 days, and we want to know the amount of material remaining after 5 years, or 1825 days. We can use the formula and plug in these values:

N = N0 * (1/2)^(1825/299) = 0.0145N0

This means that only 1.45% of the original radioactive material remains after 5 years. Therefore, the best choice is C) 1.45%.

Question 4

An investment is expected to pay 11% 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 to solve for the initial investment:

A = Pe^(rt)

where A is the final amount, P is the initial investment, r is the annual interest rate, and t is the time in years.

Plugging in the given values:

$900,000 = Pe^(0.11*25)

$900,000 = Pe^(2.75)

P = $900,000 / e^(2.75)

P = $57,535 (rounded to the nearest dollar)

Therefore, the best choice is C.

Question 5

The half-life of ¹³⁴Ba is 28.7 hours.How much of a 18.2 g sample of ¹³⁴Ba will be left after 24.00 hours? Round to the nearest hundredth of a gram.

Accepted Answer

The amount of substance left after a certain time can be calculated using the formula: $ \text{final amount} = \text{initial amount} \times \left(\frac{1}{2}\right)^{\frac{\text{time elapsed}}{\text{half-life}}} $. Here, the initial amount is 18.2 g, the time elapsed is 24 hours, and the half-life is 28.7 hours. Plugging these values into the formula gives: $ 18.2 \times \left(\frac{1}{2}\right)^{\frac{24}{28.7}} \approx 10.19 $ g.

Question 6

The table below shows the cost  (in millions of dollars) of a 30-second ad during the Super Bowl for several years from 1987 to 2006.  Use the regression feature of a graphing utility to find an exponential model for the data.Predict the cost of a 30-second ad during the Super Bowl in 2012.Round to the nearest ten thousand.

Accepted Answer

The answer of The table below shows the cost ...

Question 7

You take a three-pound package of steaks out of the freezer at 11 A.M.and place it in the refrigerator.Assume that the refrigerator temperature is  and that the freezer temperature is  Use the formula for Newton's Law of Cooling  where  is the time in hours (with  corresponding to 12 P.M.) and  is the temperature of the package of steaks (in degrees Fahrenheit).Find the time when the steaks will thaw (or reach  ).

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The answer of You take a three-pound package of steaks...

Question 8

A hunting club stocks a wildlife preserve with 20 elk.The carrying capacity of the preserve is 280 animals and the growth of the herd, allowing for the effect of controlled hunting of the elk, is expected to be modeled by the logistic curve  , where t is measured in years.After how many years will the population be 253? Round to the nearest year.

Accepted Answer

The answer of A hunting club stocks a wildlife preserve...

Question 9

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

Accepted Answer

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

Question 10

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.

Accepted Answer

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

Question 11

The decibel (dB) is defined as , where P₂ is the power of a particular signal and P₁is the power of some reference signal.In the case of sounds, the reference signal is a sound level that is just barely audible.How many dBs does a sound have if its power is 5500 times that of the reference sound? Round to the nearest tenth.

Accepted Answer

The formula for dB is: 
dB = 10 log(P/Pr)
where P is the power of the signal and Pr is the reference power.
In this case, the signal power is 5500 times the reference power. So:
dB = 10 log(5500)
dB = 37.4 (rounded to the nearest tenth)
Therefore, the answer is choice B.

Question 12

What is the half-life of a radioactive substance if 2.9 g decays to 1.80 g in 64 hours? Round to the nearest tenth of an hour.

Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, 2.9 g of the substance decays to 1.80 g in 64 hours. So, the half-life of the substance is 64 hours.

Quiz 4: Exponential and Logarithmic Functions

On the Richter scale, the magnitude of an earthquake of intensity per unit of area is given by where is the minimum intensity used for comparison.Find the magnitude (on the Richter scale) of an earthquake of intensity Round to the nearest thousandth.

Estimate the percentage of radioactive material that remains in a sample after 5 years if the half-life of the material is 299 days.Round to the nearest hundredth of a percent.

An investment is expected to pay 11% 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 half-life of 134Ba is 28.7 hours.How much of a 18.2 g sample of 134Ba will be left after 24.00 hours? Round to the nearest hundredth of a gram.

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.

What is the half-life of a radioactive substance if 2.9 g decays to 1.80 g in 64 hours? Round to the nearest tenth of an hour.

The half-life of ¹³⁴Ba is 28.7 hours.How much of a 18.2 g sample of ¹³⁴Ba will be left after 24.00 hours? Round to the nearest hundredth of a gram.

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