Because of job outsourcing, a western Pennsylvania town predicts that its public school population will decrease at the rate , where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable.

Question

Because of job outsourcing, a western Pennsylvania town predicts that its public school population will decrease at the rate  , where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable. ​

Quizplus · Accepted Answer

We can use the formula for exponential decay:
N = N0e^(-rx)

Where N is the population after x years, N0 is the initial population, r is the rate of decrease (in this case -0.12), and x is the number of years.

Plugging in the given values, we get:

N = 7800e^(-0.12*6)
N ≈ 7276

Therefore, the expected population size in 6 years is 7276, which is closest to choice D (7,276 students).

Because of Job Outsourcing, a Western Pennsylvania Town Predicts That