Question 1

Solve the problem.
-What is the intensity in  of a noise measured at 54 decibels?   . (Express in scientific notation, and round to three significant digits.)

Accepted Answer

The answer of Solve the problem.
-What is the intensity in...

Question 2

Solve the problem.
-In the formula  , A is the amount of radioactive material remaining from an initial amount I at a given time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope
Decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

The answer of Solve the problem.
-In the formula  ,...

Question 3

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-

Accepted Answer

The answer of Solve the following graphically. If necessary, round...

Question 4

Solve the problem.
-An artifact is discovered at a certain site. If it has 62% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.)

Accepted Answer

The decay of carbon-14 can be modeled by the formula $N = N_0 \times (1 - r)^t$, where $N$ is the remaining amount of carbon-14, $N_0$ is the original amount, $r$ is the annual decay rate, and $t$ is time in years. Given $N/N_0 = 0.62$ and $r = 0.000125$, solving for $t$ gives approximately 3824 years.

Question 5

Solve the equation. Round to four decimal places.
-

Accepted Answer

The answer of Solve the equation. Round to four decimal...

Question 6

Solve the problem.
-The decay of 978 mg of an isotope is given by  where t is time in years. Find the amount left after 14 years.

Accepted Answer

The answer of Solve the problem.
-The decay of 978 mg...

Question 7

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-log(x + 2) - 3 =

Accepted Answer

The answer of Solve the following graphically. If necessary, round...

Question 8

Solve the problem.
-A certain noise produces  of power, designated as S. What is the decibel level of this noise?  Round to the nearest decibel.)

Accepted Answer

The answer of Solve the problem.
-A certain noise produces ...

Question 9

Solve the problem.
-Coyotes are one of the few species of North American animals with an expanding range. The future population of coyotes in a region of Mississippi can be modeled by the equation P = 48 + 10 ln(20t + 1), where t is time in
Years. Use the equation to determine when the population will reach 160. (Round to the nearest tenth of a year.)

Accepted Answer

The answer of Solve the problem.
-Coyotes are one of the...

Question 10

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-

Accepted Answer

The answer of Solve the following graphically. If necessary, round...

Question 11

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-

Accepted Answer

The answer of Solve the following graphically. If necessary, round...

Question 12

Solve the problem.
-The half-life of an element is  yr. How long does it take a sample of the element to decay to  of its original mass? Use  where A0 is the initial amount, T is the half-life, and t is the time. (Express
Results in scientific notation, rounded to the nearest hundredth.)

Accepted Answer

The answer of Solve the problem.
-The half-life of an element...

Question 13

Solve the problem.
-A certain radioactive isotope decays at a rate of 0.125% annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

The half-life can be calculated using the formula $ t_{1/2} = \frac{\ln(2)}{r} $, where $ r $ is the decay rate in decimal form. Here, $ r = 0.00125 $. Thus, $ t_{1/2} = \frac{\ln(2)}{0.00125} \approx 555 $ years.

Question 14

Solve the equation. Round to four decimal places.
-

Accepted Answer

The answer of Solve the equation. Round to four decimal...

Question 15

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-

Accepted Answer

The answer of Solve the following graphically. If necessary, round...

Question 16

Solve the problem.
-Coffee is best enjoyed at a temperature of 115°F. A restaurant owner wants to discover the temperature T at which he should serve his coffee so that it will have cooled to this ideal temperature in 6 minutes. He discovers
That a cup of coffee served at 197°F cools to 185°F in one minute when his restaurant is at 75°F. If he maintains
The restaurant temperature at 75°F, at what temperature should he serve the coffee to meet his goal?

Accepted Answer

The rate of cooling is proportional to the difference in temperature between the coffee and the surrounding air. So, the rate of cooling is proportional to (T - 75). We know that the coffee cools from 197°F to 185°F in one minute, so the rate of cooling is (197 - 185) / 1 = 12°F per minute. We want the coffee to cool from T to 115°F in 6 minutes, so the rate of cooling must be (T - 115) / 6. Setting these two rates of cooling equal to each other, we get:(T - 75) / 1 = (T - 115) / 66(T - 75) = 1(T - 115)6T - 450 = T - 1155T = 335T = 67So, the restaurant owner should serve the coffee at 67°F.

Question 17

Solve the problem.
-Quail are game birds that fair poorly when their habitat is encroached. Wildlife biologists have discovered that the population of quail in a region can be related to the percent of the region that has been paved with roads
And parking lots. The population is  where x is the percent of the region that is paved. For a particular rural region, P = 1000 when x = 0%. Predict
What the quail population will be in this region when it becomes 8% paved.

Accepted Answer

The answer of Solve the problem.
-Quail are game birds that...

Question 18

Solve the problem.
-A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 20% of that amount?

Accepted Answer

To find the time required for a radioactive isotope to decay to a certain percentage, we use the formula: $ t = \frac{\ln(\text{final amount/original amount})}{\ln(0.5)} \times \text{half-life} $. Here, the final amount is 20% of the original, so $ t = \frac{\ln(0.2)}{\ln(0.5)} \times 1250 \approx 2902 $ years.

Question 19

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-

Accepted Answer

The answer of Solve the following graphically. If necessary, round...

Question 20

Solve the problem.
-In the formula  , A is the amount of radioactive material remaining from an initial amount I at a given time t, and k is a negative constant determined by the nature of the material. An artifact is discovered at a
Certain site. If it has 62% of the carbon-14 it originally contained, what is the approximate age of the artifact?
(carbon-14 decays at the rate of 0.0125% annually.) (Round to the nearest year.)

Accepted Answer

The answer of Solve the problem.
-In the formula  ,...

Quiz 4: Exponential and Logarithmic Functions

Solve the problem. -What is the intensity in of a noise measured at 54 decibels? . (Express in scientific notation, and round to three significant digits.)

Solve the following graphically. If necessary, round answers to the nearest thousandth. -

Solve the problem. -An artifact is discovered at a certain site. If it has 62% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.)

Solve the equation. Round to four decimal places. -

Solve the problem. -The decay of 978 mg of an isotope is given by where t is time in years. Find the amount left after 14 years.

Solve the following graphically. If necessary, round answers to the nearest thousandth. -log(x + 2) - 3 =

Solve the problem. -A certain noise produces of power, designated as S. What is the decibel level of this noise? Round to the nearest decibel.)

Solve the following graphically. If necessary, round answers to the nearest thousandth. -

Solve the following graphically. If necessary, round answers to the nearest thousandth. -

Solve the problem. -The half-life of an element is yr. How long does it take a sample of the element to decay to of its original mass? Use where A0 is the initial amount, T is the half-life, and t is the time. (Express Results in scientific notation, rounded to the nearest hundredth.)

Solve the problem. -A certain radioactive isotope decays at a rate of 0.125% annually. Determine the half-life of this isotope, to the nearest year.

Solve the equation. Round to four decimal places. -

Solve the following graphically. If necessary, round answers to the nearest thousandth. -

Solve the problem. -A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 20% of that amount?

Solve the following graphically. If necessary, round answers to the nearest thousandth. -