The number 'N' of cars produced at a certain factory in 1 day after 't' hours of operation is given by N (t) = 100t-5t^2, 0< or equal t < or equal 10. If the cost 'C' (in dollars) of producing 'N' cars is C (N) = 15,000+8000N, find the cost 'C' as a function of the time 't' of operation of the factory

Then Interpret C (t) when t=5 hours as a new function.

Question

Enzo

Mathematics

8 October, 20:09

The number 'N' of cars produced at a certain factory in 1 day after 't' hours of operation is given by N (t) = 100t-5t^2, 0< or equal t < or equal 10. If the cost 'C' (in dollars) of producing 'N' cars is C (N) = 15,000+8000N, find the cost 'C' as a function of the time 't' of operation of the factory

Then Interpret C (t) when t=5 hours as a new function.

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Answers (1)

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Cody Bird · Answer 1

Given: C (N) = 15,000 + 8000N

In the above equation simply substitute:

N (t) = 100t - 5t^2

for N

Therefore:

C (t) = 15,000 + 8000{ 100t-5t^2 }

C (t) = 15,000 + 800,000t - 40,000t^2.

at t = 5

C (5) = 15,000 + 800,000*5 - 40,000 * (5) ^2

C (5) = 3,015,000