Question

got it? 1. suppose that in 1985, there were 285 cell phone subscribers in a small town. the number of subscribers increased by 75% each year after 1985. how many cell phone subscribers were in the small town in 1994? write an expression to represent the equivalent monthly cell phone subscription increase.

Explanation:

Step1: Calculate the number of years from 1985 to 1994

The number of years $n = 1994 - 1985=9$.

Step2: Use the compound - growth formula

The compound - growth formula is $A = P(1 + r)^n$, where $P$ is the initial amount, $r$ is the growth rate as a decimal, and $n$ is the number of time periods. Here, $P = 285$, $r=0.75$, and $n = 9$. So the number of subscribers in 1994 is $A = 285\times(1 + 0.75)^9=285\times1.75^9$.
$1.75^9=1.75\times1.75\times\cdots\times1.75$ (9 times) $\approx56.697$. Then $A = 285\times56.697\approx16158$.

Step3: Find the monthly growth rate

Let the monthly growth rate be $x$. There are 12 months in a year, and in 1 year, with an annual growth rate of $1 + 0.75=1.75$, we use the formula $(1 + x)^{12}=1.75$. Solving for $x$, we get $x = 1.75^{\frac{1}{12}}-1$.

Answer:

The number of cell - phone subscribers in 1994 is approximately 16158. The expression for the equivalent monthly cell - phone subscription increase is $1.75^{\frac{1}{12}}-1$.