This exercise uses the population growth model Some bullfrogs were introduced in

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 700 600 Frog 500 population 400 200 100 0 300 t1 (2, 225 ) 1 23 4 5 6 (a) What was the initial bullfrog 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 9 years? bullfrogs (d) Estimate how long it takes the population to reach 78,000. (Round your answer to the nearest whole number.) years after introduction

Explanation / Answer

The function is of the form y= a bx

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

100= a b0

a=100

225=100 (b)2

b2=2.25

b=1.5

p(t) = 100(1.5)t

Initial bullfrog population, a=100

PoluPolulation aafter 9 years

p(t)= 100(1.5)9

=3844

78000=100(1.5)t

780=1.5t

t=16years

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