Question

An elementary school is in a growing suburb. The school’s principal estimates that the current enrollment of 750 students will increase 5% each year for the next
10 years. By what percent will the enrollment increase over 10 years?

Answer 1

Answer:

62.9% in ten years

Step-by-step explanation:

This type of growth corresponds to what is called an exponential growth, since in the expression for the number of students keep including the multiplication of the same factor as the years go by, Let's start by analyzing what happens the first year:

The initial enrollment of 750 is expected to grow by 5%, therefore after one year the enrollment should be:

After one year = Year_1 = 750 + 5% increase = $750+750*0.05=750(1+0.05)$

where we have used the decimal form of 5% as he factor 0.05 multiplying 750 (the initial enrollment) to give the increase.

After the second year, we consider a starting value of Year_1 enrollments that will increase another 5%, which gives: Year_2 = Year_1 + Year_1 * 0.05= Year_1 (1 + 0.05).

So replacing Year_1 by its original expression (750(1+0.05)) we notice that Year_2 = 750 * (1+0.05) * (1+0.05) = 750 * (1+0.05)^2

We can go on with this same reasoning and find that each year includes a new factor (1+0.05) to the new increasing enrollment.

At the end of 10 years, the number of enrollment will be:

$750*(1+0.05)^10=1221.67$

which we can round to 1222 students enrolled

This means and increase of: $\frac{1222-750}{750} =0.62933$

That is approximately 62.9%