Question

The change in bacterias population, P over t time can be modeled by one of the functions below

Answer 1

The change in a bacteria's population, P, over t time can be modeled by the following function: B.
`P_t=250(1.25)^t`.

In Mathematics, a population that increases at a specific period of time represent an exponential growth rate. This ultimately implies that, a mathematical model for any population that decreases by r percent per unit of time is an exponential equation of this form:

`P(t) = P(1 + r)^t`

Where:

• P(t) represents the population.
• t represents the time or number of years.
• P represents the initial population.
• r represents the exponential growth rate.

Since the exponential function models a bacteria's population over a period of time, it is expected that the rate of change would be an exponential growth with a growth rate that is greater than as correctly depicted by exponential function B only;

`P_t=250(1.25)^t`.

Complete Question:

The change in a bacteria's population, P, over t time can be modeled by one of the functions below:

A.
`P_t=500(0.8)^t`

B.
`P_t=250(1.25)^t`