Question

A certain forest can support a population of 800 deer. There are currently 200 deer in the forest and their population is growing at a rate of 2% per year. Complete the sequence below that models this population growth.

Answer 1

It would take 70 years for the deer population to reach 800.

An exponential function is in the form:

y = abˣ

where b is the multiplier, y, x are variables and a is the initial value.

Let y represent the population and x represent the time in years.

a = 200, b = 100% + 2% = 102% = 1.02

y = 200(1.02)ˣ

For a population of 800:

800 = 200(1.02)ˣ

ln(4) = xln(1.02)

x = 70 years

It would take 70 years for the deer population to reach 800.

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