The tuition in the school year 2012–2013 at a certain university was $11,000. For the school year 2017–2018, the tuition was $12,650. Find an exponential growth function for tuition T (in dollars) at this university t years after the 2012–2013 school year. (Round your values to four decimal places.)
To find the exponential growth function for the tuition at this university, we first need to determine the growth rate.
The initial tuition in the school year 2012-2013 was $11,000 and the tuition in the school year 2017-2018 was $12,650. To find the growth rate, we can use the formula:
$12,650 = $11,000 * (1 + r)^5
Dividing both sides by $11,000:
$12,650/$11,000 = (1 + r)^5
1.15 = (1 + r)^5
Taking the 5th root of both sides:
(1.15)^(1/5) = 1 + r
r = 0.02962
So, the growth rate r is 0.02962.
Now we can write the exponential growth function for tuition T(t) in dollars t years after the 2012-2013 school year:
T(t) = $11,000 * (1 + 0.02962)^t
T(t) = $11,000 * (1.02962)^t
Therefore, the exponential growth function for tuition at this university t years after the 2012-2013 school year is T(t) = $11,000 * (1.02962)^t.