Question

The director of a basketball camp estimates that the number N of students who will enroll in a basketball camp can be modeled by

N = −0.3t + 250,
where t is the tuition for the camp in dollars.
(a)
What is the N-intercept?
(t, N) =




(b)
Write a sentence that explains the answer to part (a) in the context of the problem.
If the tuition was $
, then
students would enroll in the basketball camp.
(c)
What is the t-intercept? (Round your answers to two decimal places when necessary.)
(t, N) =




(d)
Write a sentence that explains the answer to part (c) in the context of the problem. (Round your answers to two decimal places when necessary.)
If the tuition was approximately $
, then
students would enroll in the basketball camp.

Answer 1

Explanation:

(a) To find the N-intercept, we set t to 0 in the equation N = -0.3t + 250:

N = -0.3(0) + 250

N = 250

Therefore, the N-intercept is (0, 250).

(b) The N-intercept is the point on the graph where the tuition is $0 and represents the number of students who would enroll in the basketball camp if it were free. In this case, if the tuition was $0, 250 students would enroll in the basketball camp.

(c) To find the t-intercept, we set N to 0 in the equation N = -0.3t + 250 and solve for t:

0 = -0.3t + 250

0.3t = 250

t = 250/0.3

t ≈ 833.33

Therefore, the t-intercept is approximately (833.33, 0).

(d) The t-intercept is the point on the graph where the number of students who enroll in the basketball camp is zero and represents the tuition that would need to be charged for no students to enroll. In this case, if the tuition was approximately $833.33, no students would enroll in the basketball camp.