a) did you differentiate with respect of t, and then sub in t = 5 ?
b) P(x) = R(x) - C(x)
= 32 ln(5x+3) - x/4
P ' (x) = 32(5/(5x+3)) - 1/4
= 0 for max/min situation
160/(5x+3) = 1/4
5x+3 = 640
etc
a) The value of a computer after t years after purchase is v(t) = 1000e^(-0.45t). At what rate is the computer's value falling after 5 years?
b) Assume that the total revenue received from the sale of x items is given by R(x) = 32 ln (5x+3), while the total cost to produce x items is C(x) = x/4. Find the approximate number of items that should be manufactured so that profit, R(x) - C(x), is a maximum.
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