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.)
days
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.)
days
@Mathematics

Answer 1

\[\frac{54}{18}=3\] so it triples every three days. function will be
\[A(t)=18\times 3^{\frac{t}{3}}\]

Answer 2

if you want to know the doubling time set
\[2=3^{\frac{t}{3}}\] and solve for t via
\[\frac{t}{3}=\frac{\ln(2)}{\ln(3)}\] or
\[t=\frac{3\ln(2)}{\ln(3)}\]

Answer 3

first answer aint working