Question

The growth of a sample of bacteria can be modeled by the function b(t) =100(1.06)^t where b is the number of bacteria and t is the time in hours. What is the number of total bacteria after 3 hours? Round to the nearest whole number.

Answer 1

There are 119 bacteria after 3 hours.

Explanation:

Let be
`b(t) = 100\cdot 1.06^(t)`, where
`t` is the time, measured in hours, and
`b(t)` is the number of total bacteria, dimensionless. The number of total bacteria after 3 hours is found after evaluating the function at given function:

`b (3) = 100\cdot 1.06^(3)`

`b(3) = 119.102`

We rounded to the nearest preceeding whole number, since number of bacteria represents a discrete set. There are 119 bacteria after 3 hours.