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barxatty [35]
2 years ago
11

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?
Mathematics
1 answer:
Rudiy272 years ago
7 0

Answer:

N(t) = 972(1.015)^{t}

Growth function.

The number of students enrolled in 2014 is 1162.

Step-by-step explanation:

The number of students in the school in t years after 2002 can be modeled by the following function:

N(t) = N(0)(1+r)^{t}

In which N(0) is the number of students in 2002 and r is the rate of change.

If 1+r>1, the function is a growth function.

If 1-r<1, the function is a decay function.

In 2002, there were 972 students enrolled at Oakview High School.

This means that N(0) = 972

Since then, the number of students has increased by 1.5% each year.

Increase, so r is positive. This means that r = 0.015

Then

N(t) = N(0)(1+r)^{t}

N(t) = 972(1+0.015)^{t}

N(t) = 972(1.015)^{t}

Growth function.

Find the number of students enrolled in 2014.

2014 is 2014-2002 = 12 years after 2002, so this is N(12).

N(t) = 972(1.015)^{t}

N(12) = 972(1.015)^{12}

N(12) = 1162

The number of students enrolled in 2014 is 1162.

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