p ' (t) = 300000(-.09) e^(-.09t) + .5
= 0 for a max/min of p(x)
27000 e^(-.09t) = .5
ln both sides
ln 27000 - .09t(lne) = ln .5
ln27000 - ln .5 = .09t , since lne = 1
10.89674 = .09t
t = 121
when t = 121
p(121) = 300000e^-10.89 + 121/2
= 5.593
This result and the original equation makes no sense to me.
Was the t/2 part of the exponent?
If so, then brackets around the exponent would have been essential.
The present value of a building in the downtown area is given by the function
p(t) = 300,000e^-0.09t+(t)/2 f or 0 _< t _< 10
Find the optimal present value of the building. (Hint: Use a graphing utility to graph the function, P(t), and find the value of t0 that gives a point on the graph, (t0, P(t0)), where the slope of the tangent line is 0.
2 answers
Hello Reiny it is essential
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