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.
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.)
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