Math help asap again.?

Question

From 1990 to 1997 the number of cell phones subscribers S..(in thousands) in th u.s. can be modeled by s=5535.33(1.413)^t
where t is the numbers of years since 1990....
whats the growth factor?
and whats the annual percent increase?

in what year will the number of subscibers reach 31 million? 90 million?
how do i figure al this out?

Answer 1

5,535,333 is considered the base number of phones in the US in 1990.
41.3% is the estimated annual increase
t= the number of years

Keep replacing the "t" in the equation until you have reached or exceeded 31 million and then 90 million.
If you use excel, set up the equation like this
in A1 =5535.33*1.413^B1
in B1 = C1-1990
in C1 = enter year you want to find the number of cell phones for (2007, 2010, etc).

What this equation is doing is compounding the annual increase. If you have one year of increase, you will take your base time 1.413 (100% + 41.3%). This gives you the answer for the number of phones after one year. If you multiply by the 1.413 again, it will give you the number of phones after two years. And so on.
The equation allows you to simply skip the in-between steps required if there are many years you need to try an project for.

This is the same equation you would apply to a bank balance to find out how much money you would have in the account after a set number of years based on the interest rate. It gets a little different for monthly or daily compounding, but that is probably a lesson for another day.

Good Luck!