Question

If the number of bacteria in a colony triples every 60 minutes and the population is currently 2,000 bacteria, what will the population be in 240 minutes and is the growth modeled by a linear function or a exponential function?

Answer 1

After 240 mins, there would be:
2000 × 3^4
= 162000 bacteria
The growth would be modelled as an exponential function

Answer 2

The population in 240 minutes is 162,000 bacterias and the growth is modeled by a exponential function.

Explanation:

An exponential function is one in which the independent variable x appears in the exponent and is based on a constant a. Its expression is:

f(x)=aˣ

An exponential function, therefore, allows us to refer to phenomena that grow faster and faster. For example, the case of the development of a bacterial population: a certain species of bacteria that, every hour, triples its number of members.

The growth is modeled by exponential function. If the bacteria are tripled every hour, the base is 3, while the exponent is the change in time. Then:

f(x)=2,000*3ˣ

If
`x=(240minutes)/(60 minutes)`

x=4

f(x)=2,000*3⁴

f(x)=162,000

The population in 240 minutes is 162,000 bacterias and the growth is modeled by a exponential function.