Question

A colony of bacteria grows according to the uninhibited growth model. Suppose there is 18 g of bacteria on Monday and 54 g of bacteria on Wednesday.
(a) Find a function that gives the amount of bacteria in grams after t days. (Use the variable a to represent the initial amount.)
A(t) =


(b) What is the doubling time for the colony? (Round your answer to 2 decimal places.)

Answer 1

a. The general form of equation of an uninhibited growth model is:

A = a e^kt

where A is final amount, a is initial amount, k is constant and t is time

From Monday to Wednesday, two days have passed so t = 2, therefore calculating for constant k:

54 = 18 e^k(2)

e^2k = 3

2k = ln 3

k = 0.55

 

So the function becomes:

A(t) = a e^0.55t

 

b. Finding for t when A = 2a

2a = a e^0.55 t

0.55 t = ln 2

t = 1.26 days