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. $y = 200,000(1 + 60)^t$
b. $y = 200,000(1 + 0.6)^t$
c. $y = 200,000(1 - 60)^t$
d. $y = 200,000(1 - 0.6)^t$

Explanation:

Step1: Recall the exponential growth formula

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

Step2: Identify the values of \(a\) and \(r\)

Here, \(a = 200000\) (initial number of subscribers). The growth rate is \(60\%\), so \(r=\frac{60}{100}=0.6\).

Step3: Substitute into the formula

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

Answer:

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