This exercise uses the population growth model A culture sta

This exercise uses the population growth model A culture starts with 8700 bacteria. After 1 hour the count is 10,000. (a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.) n(t) = (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) bacteria (c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) hr

Solution

initial value of culture = 8700

after 1 hour = 10,000

formula to model number of bacteria

10,000 = 8700 e^r(1)

10,000/8700 = e^r

r = 0.139

so, formula is

n(t) = 8700 e^0.139 t

b) number of bacteria after 2 hours

n(t) = 8700 e^0.139 (2)

= 11500 bacteria

c) 2* 8700 = 8700 e^0.139t

t = 5 hour