Question

The rat population in a major metropolitan city is given by the formula n(t)measured in years since 2001 and n(t) is measured in millions.66e0.015€ where t isWhat was the rat population in 2001 ?ratsWhat does the model predict the rat population was in the year 2020 ?rats

Answer 1

The given formula is:

`n(t)=66e^(0.015t)`

Where t is measured in years since 2001 and n(t) is measured in millions.

a. What was the rat population in 2001?

Since t is measured in years since 2001, then we need to subtract 2001 from the year we want to analyze. So:

`t=2001-2001=0`

By replacing t=0 into the formula we obtain:

`\begin{gathered} n(0)=66e^(0.015*0) \\ n(0)=66e^0 \\ n(0)=66*1 \\ n(0)=66\text{ millions} \end{gathered}`

As n(t) is measured in millions, thus, the rat population in 2001 was 66000000 rats.

b. What does the model predict the rat population was in the year 2020?

t in the year 2020 is:

`t=2020-2001=19`

Then:

`\begin{gathered} n(19)=66e^(0.015*19) \\ n(19)=66e^(0.285) \\ n(19)=66*1.33 \\ n(19)=87.764294\text{ millions} \end{gathered}`

In the year 2020 the predicted rat population was 87764294 rats.