Question

The population of a town is decreasing at a rate of 1% per year. In 2000there were 1300 people. Create a function to find the populationin 2008.

Answer 1

Given that;

The population of a town is decreasing at a rate of 1% per year.

`\text{Rate r = 1\% = 0.01}`

In 2000 there were 1300 people.

`P_o=1300`

To find the population in 2008;

`P_8`

The time taken is;

`\begin{gathered} t=2008-2000 \\ t=8\text{ years} \end{gathered}`

We can calculate the population of the town in 2008 by applying the formula;

`P_8=P_o(1-r)^t`

Substituting, the given values;

`\begin{gathered} P_t=1300(1-0.01)^t \\ P_t=1300(0.99)^t \end{gathered}`

Above is a functon for calculating the population of the town at time t years after 2000.

The population of the town in the year 2008 is;

`\begin{gathered} P_8=1300(0.99)^8 \\ P_8=1,199.568 \\ P_8\approx1,200 \end{gathered}`

Therefore, the population of the town in 2008 is approximately 1,200 people.

We can also write the equation as;

`y=1300(0.99)^8`

Where y is the population of the town in year 2008.