Question

Suppose that the monthly cost C(t) of a cell phone plane is linear function of the number of minutes t used and satisfies C(0)= $60.00 and C(400)=$70.00.

(A) find the Increase in cost per minute used

(B) Find a formula of the monthly cost C(t)

(C) Find the Cost of a monthly bill if t=1000 minutes have been used.

Answer 1

• $0.025/minute
• C(t) = 60 +0.025t
• C(1000) = 85 . . . dollars

Explanation:

(A) The increase from $60 to $70 for 400 minutes is an increase of ...

$10/(400 minutes) = $0.025/minute

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(B) The monthly cost will be the cost for zero minutes plus the per-minute cost multiplied by the number of minutes:

C(t) = 60 +0.025t

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(C) The cost for 1000 minutes is ...

C(1000) = 60 +0.025·1000 = 85

The monthly bill is $85 if 1000 minutes have been used.