the current yearly rate of increase is 2.5%
The population 10 years from now is 1920 (to the nearest whole number)
Explanation:
The population two years ago = 1500 (initial value)
The present population (2 years after) = 1576
We can find the rate of increase using the information above:
Two points (0, 1500) and (2, 1576)
[tex]\begin{gathered} \text{slope = }\frac{1576-1500}{2-0} \\ \text{slope = 76/2} \\ \text{slope = 38} \end{gathered}[/tex][tex]\begin{gathered} \text{The yearly rate of increase = }\frac{rate}{in\text{itial population}} \\ \text{The yearly rate of increase = }\frac{38}{1500} \\ \text{The yearly rate of increase = }0.025\text{ = 2.5\%} \end{gathered}[/tex][tex]\begin{gathered} U\sin g\text{ exponential function:} \\ y=a(1+r)^t\text{ (since the population is increasing)} \\ a\text{ = initial value} \\ r\text{= rate of increase per year = 2.5\%} \\ t\text{ = time} \end{gathered}[/tex][tex]\begin{gathered} a\text{ = 1500} \\ r\text{ = 2.5\% = 0.025} \\ t\text{ = 10 years} \\ y\text{ = 1500(1+}0.025)^{10} \\ y=1500(1.025)^{10} \\ y\text{ = }1920.13 \end{gathered}[/tex]
Hence, the current yearly rate of increase is 2.5%
The population 10 years from now is 1920 (to the nearest whole number)
