This exercise uses the population growth model. Some bullfrogs were introduced i

Question

This exercise uses the population growth model. Some bullfrogs were introduced into a small pond. The graph shows the bullfrog population for the next few years. Assume that the population grows exponentially. In 700 600 Frog 500 population 400 300 200 100 (2, 225 1 2 3 45 6 (a) What was the initial bullfog population? bullfrogs (b) Find a function that models the bullfrog population t years since the bullfrogs were put into the pond. (Round your r value to four decimal places.) n(t) = (c) What is the projected bullfrog population after 12 years? bullfrogs (d) Estimate how long it takes the population to reach 37,000. (Round your answer to the nearest whole number.) years after introduction

Explanation / Answer

Points are (0,100),(2,225)

At t=0, n(t)=100

So initial population is 100

n(t) = n0bt

225 =100(b)2

2.25=b2

b=1.5

b. n(t) = 100(1.5)t

c.n(12) = 100 (1.5)12 =12975

d. 37000=100(1.5)t

370 = 1.5t

t= log(370)/log(1.5)=15 years

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