Modeling Population

The rabbit population started at 65,000 rabbits. The population is decreasing at a rate of 1.5% each year. Write a function r(t) to represent the rabbit population after t years.

• r(t) = 65000(1 - 0.015)^t

• r(t) = 65000(1 + 0.015)^t

• r(t) = 65000(1 - 1.5)^t

• r(t) = 65000(1 + 1.5)^t

HINT: Use your y= on the calculator to determine which one is equivalent.

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The population of a town is currently 6342 and is increasing by a rate of 1.3% each year. Which function represents the population of people, P, after t years.

• P = 6342(1 + 1.3)^t

• P = 6342(1 – 1.3)^t

• P = 6342(1 + .013)^t

• P = 6342(1 – .013)^t

The bear population in a given area is currently 1580. They anticipate the bear population to decrease by 2% each year. Which function represents the population of bears, B, after t years.

• B = 1580(0.02)^t

• B = 1580(1 – 0.02)^t

• B = 1580(1 + 0.02)^t

• B = 1580(1 – 0.2)^t

What is the equation of the following table? HINT: Use your STAT Key on your calculator

• y = 7(2)^x

• y = 4x + 7

What is the amplitude of the function?

What is the midline of the function?

What is the smallest population, and when does it occur?

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What is the population at 6pm on Wednesday?

Remember that t is counted in days, where t=0 is Saturday at midnight.

(Hint: Sunday + Monday + Tuesday + 18/24 hours on Wednesday would be what number of days as a decimal?)

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During what time interval(s) did the population exceed 600?

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