Question

A graphing calculator is recommended. A bacteria culture starts with 100 bacteria and doubles in size every half hour. (a) How many bacteria are there after 3 hours? bacteria (b) How many bacteria are there after t hours? y = bacteria

Answer 1

Answer: a) 800

b)
`y=100(2)^t`

Explanation:

The exponential growth function is represented by :-

`y=A(b)^t`, where A is initial value , b is the multiplicative rate of change and t is the time period.

Given : A bacteria culture starts with 100 bacteria and doubles in size every half hour.

i.e. A = 100 and b=2

Then, the exponential growth function to find the number of bacteris after t hours :_

`y=100(2)^t`

At x=3

`y=100(2)^3=800`

Hence, the there are 800 bacteria after 3 hours.