The tuition in the school year 2012–2013 at a certain university was $13,000. For the school year 2017–2018, the tuition was $14,950. 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.)
show your work
To find the exponential growth function for the tuition, we can use the formula for exponential growth which is:
T(t) = A * (1 + r)^t
Where:
T(t) = Tuition at time t
A = Initial tuition ($13,000)
r = Growth rate
t = Time in years
We can plug in the initial values and solve for the growth rate (r):
$14,950 = $13,000 * (1 + r)^(2017-2012)
$14,950 = $13,000 * (1 + r)^5
Dividing both sides by $13,000:
1.150769 = (1 + r)^5
Taking the fifth root of both sides:
(1 + r) ≈ 1.03298
Subtracting 1 from both sides:
r ≈ 0.03298
Therefore, the exponential growth function for the tuition T(t) at this university t years after the 2012–2013 school year is:
T(t) = $13,000 * (1 + 0.03298)^t
T(t) = $13,000 * 1.03298^t
Rounded to four decimal places:
T(t) = $13,000 * 1.03298^t
no
I apologize for the mistake. Let's correct it.
Given:
Tuition in 2012–2013 school year = $13,000
Tuition in 2017–2018 school year = $14,950
We need to find the growth rate in order to determine the exponential growth function. The growth rate (r) can be calculated using the formula:
r = (T1 / T0)^(1 / n) - 1
Where:
T1 = Final tuition ($14,950)
T0 = Initial tuition ($13,000)
n = Number of years between the two tuitions (2017 - 2012 = 5)
Substitute the values:
r = ($14,950 / $13,000)^(1 / 5) - 1
r ≈ 0.030287
Now that we have the growth rate, the exponential growth function for tuition (T) at the university t years after the 2012–2013 school year is:
T(t) = $13,000 * (1 + 0.030287)^t
T(t) = $13,000 * 1.030287^t
Therefore, the correct exponential growth function for tuition T(t) at this university t years after the 2012–2013 school year is:
T(t) = $13,000 * 1.030287^t
Please let me know if you need further assistance.
You're still wrong.
The answer is 13000 x 1.0283^t
how
I apologize for the error in my previous responses. Let's clarify the correct calculations to find the exponential growth function for tuition at the university t years after the 2012–2013 school year.
Given:
Initial tuition in 2012–2013 = $13,000
Tuition in 2017–2018 = $14,950
Number of years between 2012–2013 and 2017–2018 = 5 years
To calculate the growth rate, we use the formula:
r = (T1 / T0)^(1 / n) - 1
Substitute the values:
r = ($14,950 / $13,000)^(1 / 5) - 1
r ≈ 0.0283
Now that we have the correct growth rate, the exponential growth function for tuition (T) at the university t years after the 2012–2013 school year is:
T(t) = $13,000 * (1 + 0.0283)^t
T(t) = $13,000 * 1.0283^t
Therefore, the correct exponential growth function for tuition T(t) at this university t years after the 2012–2013 school year is:
T(t) = $13,000 * 1.0283^t
Thank you for pointing out the error, and I appreciate your attention to detail.