Question

6. The population of Mathtown grew from 10 million in 2012 to 10.5million in 2013.a. What is the annual percentage growth rate for Mathtown from 2012 to 2013?b. Use this to write down an exponential model for the population of Mathtown.c. What does the model predict for the population of Mathtown in 2015?

Answer 1

`\begin{gathered} (a)\text{percentage change=}\frac{\text{change in population}}{\in\text{itial population}}*100 \\ =(0.5)/(10)*100 \\ =5\text{ percentage} \\ (b)y=a(1+r)^x \\ y=\exp onatialgrowthfunction^{} \\ a=\text{ initial amount} \\ r=\text{ growth rate} \\ x=\text{ number of time interval} \\ y=10(1+0.05)^x \\ y=10(1.05)^x \\ (c)y=10(1.05)^5 \\ y=10*1.276 \\ y=12.76 \end{gathered}`