AnswersCollege Prep Math B - IC26Exponential, Logistic and Logarithmic Models

Exponential, Logistic and Logarithmic Models Answers

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A rabbit population is modeled by , where y is the number of rabbits after t months. How many rabbits were there initially?

Question illustration
A
1
B
4
C
20
D
50
2
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The population of an ant colony is modeled by the function , where P(t) is the population of the colony after t days. What does 1,000,000 represent?

Question illustration
A
initial population of the colony
B
population of the colony after 1 day
C
population of the colony after 10 days
D
maximum population the colony can have
3

Review the graph.

Question illustration
A
Initially there were 1,000 bacteria; the population will reach zero.
B
Initially there were 1,000 bacteria; the population will not reach zero.
C
Initially there were more than 1,000 bacteria; the population will reach zero.
D
Initially there were more than 1,000 bacteria; the population will not reach zero.
4

An investment is modeled by the function . What does 2,500 represent?

Question illustration
A
the initial investment
B
the investment value after 1 year
C
the investment value after t years
D
the percentage growth of the investment
5

A bacterial population is modeled by the function , where t is elapsed time in days. What was the initial population of bacteria?

Question illustration
A
1
B
20
C
36
D
499
6

A bacterial culture starts with a population of 750, and grows continuously at a rate of 10.43% per day. What is the approximate population after 2.5 days?

A
752 bacteria
B
770 bacteria
C
832 bacteria
D
973 bacteria
7

In a laboratory, the number of bacteria in a petri dish after t days is modeled by the function . What does 300,000 represent?

Question illustration
A
initial number of bacteria in the petri dish
B
number of bacteria in the petri dish after one day
C
number of bacteria in the petri dish at any given time
D
maximum number of the bacteria the petri dish can hold
8

Review the table of a firefly population in a laboratory.Time (in days)12345Population1,0001,3011,4771,6021,699

A
y(t) = 1,000 + 500 log(t)
B
y(t) = 1,000 + 500 log(2t)
C
y(t) = 1,000 + 1,000 log(t)
D
y(t) = 1,000 + 1,000 log(2t)
9

A manufacturer introduces a new computer, and the marketing department uses the function to predict monthly sales. Based on the model, approximately how many computers are expected to sell during the fifth month?

Question illustration
A
36
B
41
C
76
D
83
10

A piece of charcoal was unearthed at an archeological site and found to contain 10% of its original carbon-14. The half-life of carbon-14 is 5,730 years. This means that after 5,730 years, only half of the original amount of carbon-14 will remain. Which equation can be solved to determine the age of the charcoal?

A
0.10Ao = Aoe0.000121t
B
Ao = 0.10Aoe0.000121
C
0.10Ao = Aoe –0.000121t
D
Ao = 0.10Aoe –0.000121t

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