In 2011, the moose population in a park was measured to be 5,500. By 2016, the population was measured again to be 8,700. If the population continues to change exponentially,

Question

In 2011, the moose population in a park was measured to be 5,500. By 2016, the population was measured again to be 8,700. If the population continues to change exponentially, find an equation for the moose population, , as a function of , the years since 2011.   Round numbers to 3 decimal places as needed.

What does your model from above predict the moose population to be in 2025?

Answer 1

P(t) = P₀ b^t,

with b > 1.

P₀ = 5500

P(t) = 5500 b^t

In 2016,

t = 2016 - 2011 = 5

P(5) = 8700

8700 = 5500 b⁵

8700 / 5500 = b⁵

log(8700 / 5500) = 5 log(b)

[log(8700 / 5500)] / 5 = log(b)

Now take 10⁽⁾ of both sides and get b, then plug the result for b into

P(t) = 5500 b^t

To find P(t) in 2025, evaluate P(t) for t = 2025 - 2011. You should be able to finish from here.