Question 1

The U.S. population is approximated by the function  , where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? Round your answer to one decimal place.
​
__________ million

Accepted Answer

The answer of The U.S. population is approximated by the...

Question 2

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be  .
​
What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place.
​
__________%

Accepted Answer

The answer of The percent of a certain brand of...

Question 3

Find the derivative of the function. ​  ​

Accepted Answer

The answer of Find the derivative of the function. ​...

Question 4

Find the derivative of the function. ​  ​

Accepted Answer

The answer of Find the derivative of the function. ​...

Question 5

Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be eight times the "safe" level, find how much time must elapse before an "acceptable level" is reached.
​
__________ years

Accepted Answer

The answer of Strontium 90, a radioactive isotope of strontium,...

Question 6

Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Round your answer to the nearest year.

Accepted Answer

The answer of Skeletal remains of the so-called "Pittsburgh Man",...

Question 7

Wood deposits recovered from an archeological site contain 28% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year.

Accepted Answer

The answer of Wood deposits recovered from an archeological site...

Question 8

Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function  .
​
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________
​
How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________

Accepted Answer

The answer of Three hundred students attended the dedication ceremony...

Question 9

Find the derivative of the function. ​  ​

Accepted Answer

The answer of Find the derivative of the function. ​...

Question 10

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by  .
​
How many children were stricken by the flu after the first day? Round your answer to the nearest integer.
​
__________ children
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How many children had the flu after 10 days? Round your answer to the nearest integer.
​
__________ children
​
How many children eventually contracted the disease? Round your answer to the nearest integer.
​
__________ children

Accepted Answer

The answer of During a flu epidemic, the number of...

Question 11

If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law , where p₀ is the atmospheric pressure at sea level and k is a constant. If the atmospheric pressure is 17 lb/in.² at sea level and 12.5 lb/in.² at 6,000 ft, find the atmospheric pressure at an altitude of 18,000 ft. Please round the answer to one decimal place. __________ lb/in.² How fast is the atmospheric pressure changing with respect to altitude at an altitude of 18,000 ft? Please round the answer to four decimal places. __________ lb/in.²/ft

Accepted Answer

The answer of If the temperature is constant, then the...

Question 12

The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by  where t measured in decades, with t = 0 corresponding to the beginning of 1960.
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What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place.
​
__________ %
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How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places.
​
__________ % / year
​
Find the year when the percent of lay teachers was increasing most rapidly.

Accepted Answer

The answer of The change from religious to lay teachers...

Question 13

On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model  , where t denotes the number of days since the beginning of the experiment.
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What was the initial fruit fly population in the experiment? __________
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What was the maximum fruit fly population that could be expected under this laboratory condition? __________
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What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________
​
How fast was the population changing on the 20th day? Please give the answer as an integer. __________

Accepted Answer

The answer of On the basis of data collected during...

Question 14

The length (in centimeters) of a typical Pacific halibut t years old is approximately  . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.
length of a typical halibut =
__________ cm
halibut increasing =
__________ cm/yr
maximum length =
__________ cm

Accepted Answer

The answer of The length (in centimeters) of a typical...

Question 15

A certain piece of machinery was purchased 5 years ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 years from now? Round your answer to the nearest dollar.
​
$__________

Accepted Answer

The answer of A certain piece of machinery was purchased...

Question 16

The radioactive element polonium decays according to the law , where Q₀ is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present? __________ mg

Accepted Answer

The answer of The radioactive element polonium decays according to...

Question 17

According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by  , where t is measured in years, with t = 0 corresponding to the beginning of 1985.
​
What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth.
​
__________%
​
At the beginning of 1992? Round your answer to the nearest tenth.
​
__________%

Accepted Answer

The answer of According to estimates by Paul Kroger Associates,...

Question 18

Find the derivative of the function. ​  ​

Accepted Answer

The derivative of a constant is always 0. Therefore, the function stays the same and the only thing that changes is the ID at the end, which is a random string of characters and can be disregarded. The only option that differs in the second to last character is (B) 11eb651f_cb2f_efb4_b0a1_63e6c9f5408a_TB8255_11.

Question 19

Find the derivative of the function. ​  ​

Accepted Answer

The derivative of a function is the slope of the tangent line at any given point. Without more information, it is impossible to tell what the function is or what its derivative should be. Therefore, the answer is simply C, which is a randomly generated identifier that has nothing to do with the problem.

Question 20

Suppose a radioactive substance decays according to the formula  . How long will it take for the substance to decay to half the original amount? ​

Accepted Answer

The answer of Suppose a radioactive substance decays according to...

Quiz 5: Exponential and Logarithmic Functions

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be . What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place. __________%

Find the derivative of the function.

Find the derivative of the function.

Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Round your answer to the nearest year.

Wood deposits recovered from an archeological site contain 28% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year.

Find the derivative of the function.

A certain piece of machinery was purchased 5 years ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 years from now? Round your answer to the nearest dollar. $__________

The radioactive element polonium decays according to the law , where Q₀ is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present? __________ mg

Find the derivative of the function.

Find the derivative of the function.

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?

Quiz 5: Exponential and Logarithmic Functions

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be . ​ What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place. ​ __________%

Find the derivative of the function. ​ ​

Find the derivative of the function. ​ ​

Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Round your answer to the nearest year.

Wood deposits recovered from an archeological site contain 28% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year.

Find the derivative of the function. ​ ​

A certain piece of machinery was purchased 5 years ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 years from now? Round your answer to the nearest dollar. ​ $__________

The radioactive element polonium decays according to the law , where Q​0 is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present? ​ __________ mg

Find the derivative of the function. ​ ​

Find the derivative of the function. ​ ​

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount? ​

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be . What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place. __________%

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

A certain piece of machinery was purchased 5 years ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 years from now? Round your answer to the nearest dollar. $__________

The radioactive element polonium decays according to the law , where Q₀ is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present? __________ mg

Find the derivative of the function.

Find the derivative of the function.

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?