Question

select the correct answer. in the year 2000, there were 200,000 cell - phone subscribers in a city in new york. the number of subscribers increased by 60 percent per year after 2000. which equation can be used to model the number of subscribers, y, in the city t years after 2000? a. y = 200000(1 + 60)^t b. y = 200000(1 + 0.6)^t c. y = 200000(1 - 60)^t d. y = 200000(1 - 0.6)^t

Explanation:

Step1: Recall compound - growth formula

The formula for exponential growth is $y=a(1 + r)^t$, where $a$ is the initial amount, $r$ is the rate of growth as a decimal, and $t$ is the time.

Step2: Identify values from the problem

The initial number of subscribers $a = 200000$, and the rate of growth $r=60\%=0.6$, and the time is $t$ years after 2000.

Step3: Substitute values into formula

Substituting $a = 200000$ and $r = 0.6$ into $y=a(1 + r)^t$, we get $y = 200000(1+0.6)^t$.

Answer:

B. $y = 200000(1 + 0.6)^t$