Question

A culture started with 3000 bacteria. After 2 hours it grew to 3300 bacteria. Predict how many bacteria will be present after 16 hours. Round your answer to the nearest whole number.

Answer 1

`6,430\ bacteria`

Explanation:

we have a exponential function of the form

`y=a(1+r)^(x)`

where

y is the population of bacteria

a is the initial value

r is the rate of growth

x is the number of hours

we have

a=3,000 bacteria

`y=3,000(1+r)^(x)`

For x=2, y=3,300

substitute

`3,300=3,000(1+r)^(2)`

`(3,300/3,000)=(1+r)^(2)`

Apply square root both sides

`1+r=√(3.3/3)`

`r=√(3.3/3)-1`

`r=0.0488`

`r=4.88\%`

substitute in the equation

`y=3,000(1+0.0488)^(x)`

`y=3,000(1.0488)^(x)`

Predict how many bacteria will be present after 16 hours

For x=16 hours

substitute

`y=3,000(1.0488)^(16)`

`y=6,430\ bacteria`