Question

Harry started a school in the year 2000. The number of students was 500 in the beginning and is increasing at a rate of 13% each year. Use a graph to predict the number of students in the year 2020.

Answer 1

The predicted number of students in the year 2020 is 5762.

Explanation:

Given,

The initial number of students, P = 500 ( In year 2000),

Also, it is increasing at a rate of 13% each year.

So, the rate of increasing = 13 % = 0.13,

Thus, the number of students after x years since 2000,

`A=P(1+r)^x`

`=500(1+0.13)^x`

`=500(1.13)^x`

Which is an exponential growth function,

Having y-intercept = (0,500),

And, horizontal asymptote x-axis,

By making the graph of the above function we observed that,

It is passes from the point (20, 5761.544 )

Hence, the predicted number of students in the year 2020 is 5762. ( number can not be in decimals )