4:09 PM webassign.net \"IT-Mobile Need Help? This exercise uses the population g

Question

4:09 PM webassign.net "IT-Mobile Need Help? This exercise uses the population growth model The bat population in a certain Midwestern county was 230,000 in 2012, and the observed doubling time for the population is 31 years. (a) Find an exponential model ns-n-for the population t years after 2012. (b) Find an exponential model -n for the population t years after 2012. (Round your r value to four decimal places.) -0.3010x (c) Sketch a graph of the population at time t. 400000 400000 120000 0240 O 10 20 40 400000 800000 1020340 (d) Estimate how long it takes the population to reach 2 million. (Round your answer to two decimal places.) x yr Need Help? 9os

Explanation / Answer

a) 460,000 = 230,000^(31/a)

First, determine "a" based on the information provided.
This is one method, you may have been taught some other method:
460,000 = e^((31/a) ln(230,000))
ln (460,000) = (31/a) ln (230,000)
ln (460,000) / ln (230,000) = 31/a
1.056144 = 31/a
29.4 = a

So,
n(t) = 230,000^(t/29.4)

b) For this one, first determine "r" based on what you know:
b) 460,000 = 230,000 e^(r*31)
ln (460,000/230,000) = r*31
0.693147 = r*31
0.0224 = r
n(t) = 230,000 e^(0.0224*t)

d) The population will reach 2 million in:
2,000,000 = 230,000 e^(0.0224*t)
ln (2,000,000 / 230,000) = 0.0224*t
2.16282 = 0.0224*t
96.6 years = t

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