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Hi, H/A. As usual, I will be taking full advantage of our resident math gurus in my time of need. Thanks in advance!
The population of Austria, P, in millions, is given by
P(t) = 5:6 (0.994)^t where t is time in years since 2000. How fast (in people/year) will it be changing in 2010?
I know that the answer is
P'(t) = 5.6 (0.994) ln (0.994)
= -31,733 people/year
I do not know where the ln (0.994) bit comes from. Is it some special property of the derivative of a number ^10? Something to do with the chain rule? Thanks again. I'll be adding problems as they come along.
The average cost per item to produce q items is given by a(q) = q^2 - 90q +3500. Find the minimum value of the marginal cost. (Hint: First find the total cost C(q), and then MC(q). Then minimize MC(q).)
So to get C(q) I would just multiply the a(q) function by q, since (average cost per unit) times (number of units) = (total cost), right?
That gives me C(q) = q^3 - 90q + 3500q.
Marginal cost would be the derivative, correct? C'(q) = 3q^2 - 180q + 3500
I believe the next step is to set the function equal to zero to get the critical point(s). 0 = 3q^2 - 180q + 3500 3500 = 3q^2 - 180q
And here I am stuck. Thanks again for the assistance.