Question

In 2012 the population at a middle school was 695 students. In 2016, the population had grown to 825 students. Assuming a constant rate of change, predict the population of the school in 2018.




890 students

725 students

850 students

760 students

Answer 1

Answer:

These kind of problem can be modeled by using the following equation

y = Po*e^(k*(t-to))

Where

Po = initial population

to = year of the initial population

y = Number of students at current year

k = constant rate of change

t = time in years

In 2012

695 = Po*e^(k*(2012 - 2012))

Po = 695

In 2016

825 = 695.e^(k*(2016-2012))

825/695 = e^(k*(4))

ln(825/695) = 4*k

k = ln(825/695) / 4

k = ln(825/695) / 4

k = 0.04287

in 2018

y = 695*e^(0.04287*(2018-2012))

y = 695*e^(0.04287*(6))

y = 695*e^(0.257)

y = 695*1.293

y = 898.85

approximately

899 students