This exercise uses the population growth model. The graph shows the deer populat

Question

This exercise uses the population growth model. The graph shows the deer population in a Pennsylvania county between 2010 and 2014. Assume that the population grows exponentially. What was the deer population in 2010? Find a function that models the deer population t years after 2010. (Enter your answer in the form n_0 e^rt. Round your r value to four decimal places.) n(t) = What is the projected deer population in 2024? (Round your answer to the nearest thousand.) Estimate how long it takes the population to reach 400,000. ()

Explanation / Answer

a) part is correct

b) n = noe^rt

no is the intial population in 2010 : no = 20,000

(4, 31000).find the value r:

31000 = 20,000e^4r

ln(31/20) = 4r

r =0.1095

So, n = 20,000e^(0.1095t)

c) 2024 year ; t = 14

n = 20000e^(0.1095*14)

= 92723.53 = 930000

d) 400,000 = 20,000e^(0.1095t)

20 = e^(0.1095t)

take natural log on both sides:

ln(2) = 0.1095t

t = 27.36 yrs

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