Answer:
4.4 years
Step-by-step explanation:
Next time, please share the answer choices.
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.
