The exponential growth model for the future population is:
[tex]P(x)=1600(1.123)^x[/tex]The population will be 2266 in 3 years
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:
[tex]P=P_o(1+r)^x[/tex]Substitute P₀ = 1600 and r = 0.123 into the equation to get the exponential growth model for the future population
[tex]\begin{gathered} P(x)=1600(1+0.123)^x \\ \\ P(x)=1600(1.123)^x \end{gathered}[/tex]Substitute x = 3 into the model to find the student population in 3 years
[tex]\begin{gathered} P(3)=1600(1.123)^3 \\ \\ P(3)=2265.9965872 \\ \\ P(3)=2266 \end{gathered}[/tex]The population will be 2266 in 3 years
