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QuestionThe function C(t)=25.50t−16.75C(t)=25.50 t-16.75 gives the cost for concert tickets.
1. Calculate C(4)C(4).
2. Explain what C(4)C(4) means.
3. Is C(6.5)C(6.5) reasonable in this context?

Studdy Solution

STEP 1

Assumptions1. The function C(t)=25.50t−16.75C(t)=25.50 t-16.75 represents the cost of buying tt tickets to the concert with a $16.75\$16.75 coupon. . The cost, CC, is measured in dollars for tt tickets.
3. The function is valid for all real values of tt.

STEP 2

To find the value of C(4)C(4), we substitute t=4t=4 into the function.
C(4)=25.50×4−16.75C(4) =25.50 \times4 -16.75

STEP 3

Calculate the value of C()C().
C()=25.50×−16.75=$85.25C() =25.50 \times -16.75 = \$85.25

STEP 4

In the context of the problem, C(4)C(4) represents the cost of buying4 tickets to the concert with a $16.75\$16.75 coupon.

STEP 5

To find the value of C(.5)C(.5), we substitute t=.5t=.5 into the function.
C(.5)=25.50×.5−16.75C(.5) =25.50 \times.5 -16.75

STEP 6

Calculate the value of C(6.5)C(6.5).
C(6.5)=25.50×6.5−16.75=$149.50C(6.5) =25.50 \times6.5 -16.75 = \$149.50

STEP 7

In the context of the problem, C(6.5)C(6.5) represents the cost of buying6.5 tickets to the concert with a $16.75\$16.75 coupon. However, it's not reasonable to buy half a ticket, so the value of C(6.5)C(6.5) is not reasonable in the context of the problem.
The solution is1. The value of C(4)C(4) is $85.25\$85.25.
2. C(4)C(4) represents the cost of buying4 tickets to the concert with a $16.75\$16.75 coupon.
3. The value of C(6.5)C(6.5) is not reasonable in the context of the problem because you cannot buy half a ticket.

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