Consider the cost of college tuition after t years if it is $4000 now and is increasing by 10% each year

Answer 1

So with a situation like this, you're going to be looking at an exponential rate of growth because it's growing by a percentage, rather than a single amount every year. (For example, there's a difference between something growing by 10% every year versus $10 a year, the latter of which would be an example of linear growth).

For exponential growth, the formula tends to look like f(t) = a(1+ r)^t where f(t) is the final amount, a is your initial (starting) amount, r is your rate of change, and t is the length of time that has passed.

In this case, your initial amount a is $4,000, and your rate is 10% or 0.10.

So your equation will look like f(t) = 4,000(1+0.10)^t

Answer 2

C(t) = 4000(1.10)^t