This exercise uses the population growth model The graph sho

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. ()

Solution

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