Question

The current student population of Philadelphia is 2300. If the population increases at a rate of 15.1% each year. What will the student population be in 6 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 6 years? (Round to nearest student)

Answer 1

Given

`\begin{gathered} initial\text{ population\lparen a\rparen=2300} \\ r=15.1\text{\%} \\ t=6\text{ years} \end{gathered}`

Step-by-step explanation

The exponential growth model is given as;

`P(x)=a(1+r)^t`

Therefore, the exponential growth model becomes

`\begin{gathered} p(x)=2300(1+(15.1)/(100))^6 \\ =2300(1+0.151)^6 \\ =2300(1.151)^6 \\ =5347.85690 \end{gathered}`

Answer 1: Exponential model

`P(x)=2300(1.151)^x`

Answer 2: The population in 6 years

`5348`