Question

A graduate school plans to increase its enrollment capacity by developing its facilities and the programs it offers. Their enrollment capacity this year was 120 graduate students. Beginning next year, the school plans to triple this number every year, with a target enrollment capacity of 3,240 students. Which equation represents this situation, and after how many years, t, will the graduate school be able to achieve its target enrollment capacity?

Answer 1

Answer:

4.4 years

Step-by-step explanation:

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In this case, the beginning enrollment capacity was 120.  The rate of increase was 3.00, the terminal enrollment cap 3,240.  We let t represent the number of years:

3,240 students = (120 students)(3.00)^t

We need to solve this for t, the number of years required before enrollment will hit 3,240 students.

Solve 3240 = 120(3)^t for t:

Divide both sides by 120, obtaining 27.

Then we have

127 = 3^t

Logarithms are the best tool to use here to find t.  Take the natural log of both sides:

log 127 = t log 3.  Solving for t:  t = (log 127) / (log 3), or t = 2.104 / 0.477 = 4.41

Thus, starting at 120 students, enrollment reached 3,240 students in 4.4 years.