We have been given that the number of students enrolled at a college is 18,000 and grows 4% each year. We are asked to find number of students after 22 years.
We will use exponential growth function to solve our given problem.
We know that an exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where
y = Final value,
a = Initial value,
r = Growth rate in decimal form,
x = Time
[tex]4\%=\frac{4}{100}=0.04[/tex]
[tex]y=18,000\cdot (1+0.04)^x[/tex]
[tex]y=18,000\cdot (1.04)^x[/tex]
To find number of students after 22 years, we will substitute [tex]x=22[/tex] in our function.
[tex]y=18,000\cdot (1.04)^{22}[/tex]
[tex]y=18,000\cdot (2.3699187915049464)[/tex]
[tex]y=42,658.53824[/tex]
[tex]y\approx 42,659[/tex]
Therefore, there will be approximately 42,659 students after 22 years.
