Question

Researchers use formula f(t) = Pe^rt to model the population of fruit flies growing exponentially after t days.
Measurements show that f(0) = 30 and
f(5) = 1620

a) Find a function of the form
f(t) = Pe^rt that models the fruit fly population after t days.

b) When the function f is expressed in the f(x) = Pa^x, the constant a is the growth factor. Find the growth factor.

c) When will there be 18,000 fruit flies?

Answer 1

f(0) = 30 , so
30 = P(e^0)
P = 30

f(5) = 1620

1620 = 30 e^(5r)
54 = e^(5r(
ln 54 = ln e^(5r)
ln54 = 5r
r = ln54/5 = .7978

f(t) = 30 e^(.7978t)

replace f(t) with 18000 and solve for t