Question

A population grows according to an exponential growth model the initial population is 13 and the grows by 6% each yearFind an explicit formula for the population growth use that formula to evaluate the population after seven yearsRound your answer to two decimal places

Answer 1

The initial population given is

`=13`

The percentage growth rate is

`\begin{gathered} r=6^{} \\ r=(6)/(100)=0.06 \end{gathered}`

The Exponential function is given as

`\begin{gathered} y=ab^x \\ \text{where,} \\ a=\text{initial growth}=13 \\ b=\text{growth rate=(1+r)} \\ x=Number\text{ of years=11} \end{gathered}`

By substituting the values, we will have the exponential formula to be

`\begin{gathered} y=ab^x \\ y=a(1+r)^x \\ y=a(1+0.06)^x \\ y=a(1.06)^x \end{gathered}`

By substituting the values of a and x in the formula above, we will have

`\begin{gathered} y=a(1.06)^x \\ y=13(1.06)^(11) \\ y=13*1.898298558 \\ y=24.67788126 \\ y\approx(2\text{ d.p)} \\ y\approx24.68 \end{gathered}`

Therefore,

The final answer is = 24.68