Word problem: Dealing with functions

The circulation of a magazine is currently 100,000, and decreasing. They have hired a consulting firm who have come up with a brilliant plan to turn the magazine's fortunes around, and claim that the circulation (in thousands) after t years will be

C(t) = 100 - 30t - 5t^2 - 0.2t^3

]

[ The model is only valid for t >(or equal) 0, and C(t) >(or equal) 0. ]

a) What is the circulation after 8 years?

b) Use the derivative to estimate the circulation after 9 years.

c) When does the circulation reach 100,000 again?

d) What is the maximum circulation?

Please tell me if I'm on the right track:

a) I put 8 for t and solve.

b) The derivative is - 30 + 10t - .6t^2. Now in this I put 9 for t and solve

c) Have no idea. 100, 000 = C(t)

d) No clue.

Thanks. (Heart)

Re: Word problem: Dealing with functions

Quote:

Originally Posted by

**hollylovespunk**

a) I put 8 for t and solve.

Yep.

Quote:

Originally Posted by

**hollylovespunk**

b) The derivative is - 30 + 10t - .6t^2. Now in this I put 9 for t and solve

This will give you the rate of change in the 9th year.

Quote:

Originally Posted by

**hollylovespunk**

c) Have no idea. 100, 000 = C(t)

Yep, solve for t

Quote:

Originally Posted by

**hollylovespunk**

d) No clue.

Solve for the C'(t) = 0

Re: Word problem: Dealing with functions

Thank you pickslides. Everything makes sense except d. How does solving for C'(t) = 0 tell us the maximum circultation? If you could just explain the logic I will solve these so you guys can check my work.

Re: Word problem: Dealing with functions

C'(t) gvies the gradient, when the gradient is zero implies a maximum or minimum.