Question

The current student population of Tucson is 2500. If the population increase at a rate of 15% each year. What will the student population be in 10 years?Write an exponential growth model for the future population (y) in terms of time x: y=What will the population be in 10 years? (Round to nearest student)

Answer 1

Explanation

Let's assume that we have a certain quantity y that increases at a rate of p% every x years. If the initial quantity (i.e. the quntity at x=0) is "a" then the value of y after x years is given by:

$y=a\cdot(1+\frac{p}{100})^x$

We are told that the current student population of Tucson is 2500 and that it will increase at a rate of 15% per year. Then the student population after x years is given by:

$\begin{gathered} y=2500\cdot(1+\frac{15}{100})^x \\ y=2500\cdot1.15^x \end{gathered}$

Then the student population after 10 years is given by:

$y=2,500\cdot1.15^{10}=10113.89$Answer

Then the answers are:

$y=2500\cdot1.15^x$

The population will be 10114.