i need help solving this

Question

This exercise uses the exponential growth model.

The count in a culture of bacteria was 200 after 2 hours and 12,800 after 6 hours.

(a)

What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.)

%

(b)

What was the initial size of the culture? (Round your answer to the nearest whole number.)

bacteria

(c)

Find a function that models the number of bacteria n(t) after t hours. (Enter your answer in the form

n0ert.

Round your

n0

value to the nearest whole number. Round your r value to two decimal places.)

n(t) =

(d)

Find the number of bacteria after 4.5 hours. (Round your answer to the nearest hundred.)

bacteria

(e)

After how many hours will the number of bacteria reach 25,000? (Round your answer to two decimal places.)

hr

Answer 1

200=Pe^2r

1280=Pe^6r

1280/200= e^4r

ln6.4 =4r

r= ln6.4/4=about .464 = 46% per hour rate of growth

P=about 79= initial amount of bacteria

200=79e^.5ln6.4

n(t) = 79e^(ln6.4)t/4

n(t) = 79e^.46t = number of bacteria after t hours

in 4.5 hours

n(4.5)= 79e^.46(4.5) =about 600

it reaches 25000

when

25000=79e^.46t

25000/79 = e^.46t

t = (ln25000/79)/.46= about 12.41 hours