help please i dont underrstand

Question

The student population in the Greenville school system is increasing about 10% each year. This year there are 3,120 students in the Greenville school system. If this trend continues, which of the following is closest to the number of students who will be in this school system 3 years from now?

Answer 1

Here we utilize an exponential to realize the time factor.

To get us started, let's write the formula for the number of students in each year:

Year 0 --> Year 0 * (1.1)⁰ = Year 0 * 1 = 3,120 students

Year 1 --> Year 0*(1.1) = Year 0 * (1.1)¹ = 3,432 students

Year 2 --> Year 1 * (1.1) = Year 0 * (1.1) * (1.1) = Year 0 * (1.1)² = 3,775

Year 3 --> Year 2 * (1.1) = Year 0 * (1.1) * (1.1) * (1.1) = Year 0 * (1.1)³ = 4,153

As you can see, we can use the formula:

Year n = Year 0 * (1.1)ⁿ to determine the number of students in any year.

Answer 2

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