Question

A bacteria colony starts with 5 bacteria at the beginning and triples every hour. How would

you write an explicit equation to model this situation?

A. f(x) = 3.5*

B. f(x) = 3x + 5

C. f(x) = 5x + 3

D. f(x) = 5.3%

Answer 1

B. f(x) = 3x + 5

Explanation:

Initial amount of bacteria N0 = 5 bacteria's

If the triple every hour,

The increase in bacteria in the colony after x hour will be 3*x =3x

x is the amount of hour.

Total amount of bacteria in the colony after x hour will be N0 + 3x

Let f(x) be the total amount of bacteria in the colony after x hour

f(x) = N0+3x

Since N0 = 5

f(x) = 5+3x

Re-arrange

f(x) = 3x + 5

Hence an explicit formula to model the equation is f(x) = 3x + 5