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In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write an exponential function to model the situation, then find the number of students enrolled in 2014. Is this considered growth or decay?

Step-by-step explanation:

The growth factor is 1 added to the growth rate of 1.5%, so is 1.015. This factor is applied each year. So the number of students will be the original number multiplied by this factor as many times as there are years (after 2002).

Repeated multiplication is signified using an exponent. The function can be written as ...

  n(t) = 972×1.015^t

In 12 years after 2002, the number of students is modeled as ...

  n(12) = 972×1.015^12 ≈ 1162 . . . students in 2014

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When the change is described as "increased by ...", it means the function is modeling growth. If the population were to decrease, it would be considered decay. That is, the "growth factor" is greater than 1 for growth, and less than 1 for decay. 1.015 is greater than 1, so this is considered growth.

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