Question

The current student population of Memphis is 2900. If the population increases at a rate of 10.7% each year. What will the student population be in 10 years?Write an exponential growth model for the future population P(x) where x is in years:P(x)=What will the population be in 10 years? (Round to nearest student)

Answer 1

Given:

Current population = 2900

rate of increase = 10.7% each year

The exponential growth formula is defined as:

$\begin{gathered} P\text{ = P}_0e^{rt} \\ Where\text{ P}_0\text{ is the initial population} \\ r\text{ is \% growth rate} \\ and\text{ t is time in years} \end{gathered}$

Substituting the given values:

$P(x)\text{ = 2900e}^{0.107x}$

Hence, the exponential model is:

$P(x)\text{ = 2900e}^{0.107x}$

The population in 10 years

We substitute 10 for x in the equation above and solve:

$\begin{gathered} P(x=10)\text{ = 2900e}^{0.107\times10} \\ =\text{ 8454.6005} \\ \approx\text{ 8455 students} \end{gathered}$

Hence, the population of the students after 10 years would be 8455 students