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
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.)
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5 answers
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.
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
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.
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.