Question

The bird population on an island is declining at a rate of 2.2% per year. The population was 3500 in the year 2016. Which answer is the best prediction of the population in the year 2022?A) 2730B) 3063C) 3132D) 3423

Answer 1

An exponential decay function is given in the form:

`y=a(b)^x`

where a is the initial value and b is the growth factor calculated using the formula:

`b=1-r`

and r is the decay rate.

The question provides the decay rate is 2.2%. Therefore, we have that:

`r=(2.2)/(100)=0.022`

Thus, the growth factor is:

`b=1-0.022=0.978`

If we take 2016 as the first year, then we have that:

`a=3500`

Thus, the function will be:

`y=3500(0.978)^x`

The population prediction can be gotten by using x as the number of years from 2016 the year in consideration is.

Therefore, for 2022, the number of years will be:

`x=2022-2016=6`

Hence, the population prediction will be:

`\begin{gathered} y=3500(0.978)^6 \\ y=3062.67\approx3063 \end{gathered}`

The SECOND OPTION is correct.