This exercise uses the population growth model. The bat population in a certain Midwestern county was 240,000 in 2012, and the observed doubling time for the population is 32 years.

Question

(a) Find an exponential model n(t) = n₀2^t/a  for the population t years after 2012. 

n(t) = 

 

(b) Find an exponential model n(t) = n₀e^rt for the population t years after 2012. (Round your r value to four decimal places.) 

n(t) = 

(c) Estimate how long it takes the population to reach 2 million. (Round your answer to two decimal places.) 

Answer 1

240K in 2012

doubling time = 32

480K = 240Ke^32r solve for r

2 = e^32r

ln2 = 32r

r = ln2/32 = about .0217 = 2.17% growth rate

2 million = 2,000,000 = 2000K

2,000K = 240Ke^(ln2/32)t solve for t

ln(200/24) = (ln2/32)t

t = ln(25/3)/ln2/32

t = about 97.8846 +2012 = 2109.88 = 2110 to reach 10 million