Question

The current student population of New York City is 1600. If the population increases at a rate of 12.3% each year. What will the student population be in 3 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 3 years? (Round to nearest student)

Answer 1

Answer:

The exponential growth model for the future population is:

`P(x)=1600(1.123)^x`

The population will be 2266 in 3 years

Step-by-step explanation:

The initial population, P₀ = 1600

The rate, r = 12.3% = 12.3/100

r = 0.123

Time, x = 3 years

The exponential growth model is of the form:

`P=P_o(1+r)^x`

Substitute P₀ = 1600 and r = 0.123 into the equation to get the exponential growth model for the future population

`\begin{gathered} P(x)=1600(1+0.123)^x \\ \\ P(x)=1600(1.123)^x \end{gathered}`

Substitute x = 3 into the model to find the student population in 3 years

`\begin{gathered} P(3)=1600(1.123)^3 \\ \\ P(3)=2265.9965872 \\ \\ P(3)=2266 \end{gathered}`

The population will be 2266 in 3 years