Question

A scientist is observing bacterial population growth on a microscope slide. Initially there are 72 organisms. The scientist notes that the population triples every hour. What function, P(t), can she use to describe the changes in population as a function of time, in hours, t? Your equation should start with P(t)=

Answer 1

72(3^t)

Explanation:

In 1 hour,

72(3)

In 2 hours

72(3)(3) = 72(3)²

.

.

.

In t hours,

72(3^t)

Answer 2

`P(t)=72(3)^t`

Explanation:

We have to find an equation of the form
`f(x)=ab^x`, where a is the initial value, b is the rate, and x is the time.

Here, the initial amount if 72, so a = 72. We also know that the population triples every hour, which means b = 3. Plug these in:

`P(t)=ab^t`

`P(t)=72(3)^t`