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?

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?)

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