Question

The population at Bishop High School is 2000 students in 2011. Every year the population decreases by 50 students

Write a function to describe the population of Bishop High School after t years if t=0 in 2011


Find the projected population of the high school in 2015


When will the population be 1600 students?

Answer 1

• Let p be the population at t be the number of years since 2011. Then,
  `p=2000-50t`

• The projected population of the high school in 2015=1800
• In 2019 the population be 1600 students

Explanation:

Given: The population at Bishop High School students in 2011 =2000

Also, Every year the population decreases by 50 students which implies the rate of decrease in population is constant.

So, the function is a linear function.

Let p be the population at t be the number of years since 2011.

Then,
`p=2000-50t`

So at t=0, p=2000

In year 2015, t=4, substitute t=4 in the above equation ,we get

`p=2000-50(4)\\\Rightarrow\ p=2000-200\\\Rightarrow\ p=1800`

Hence, the projected population of the high school in 2015=1800

Now, put p=1600 in the function , we get

`1600=2000-50t\\\Rightarrow50t=2000-1600\\\Rightarrow50t=400\\\Rightarrow\ t=(400)/(50)\\\Rightarrow\ t=8`

Now, 2011+8=2019

Hence, in 2019 the population be 1600 students