Answer:
The population of the students at the University after 5 years is 442.
Step-by-step explanation:
Given:
Current population of students is, [tex]P_o=400[/tex]
Growth rate is, [tex]r=0.02[/tex]
Time after which population is needed is, [tex]t=5\ years[/tex]
Let 'P' be the population after 't' years.
Population growth is an exponential growth and the equation to determine the population after 't' years is given as:
[tex]P=P_oe^{rt}[/tex]
Now, plug in 400 for [tex]P_o[/tex], 0.02 for 'r', 5 for 't' and solve for 'P'. This gives,
[tex]P=(400)e^{0.02\times 5}\\\\P=400\times e^{0.1}\\\\P=400\times 1.1052\\\\P=442[/tex]
Therefore, the population of the students at the University after 5 years is 442.
