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) $y=100(2)^t$

Step-by-step 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.