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

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.
Hello Reiny it is essential
Similar Questions
    1. answers icon 0 answers
    1. answers icon 2 answers
  1. The present value of a building in the downtown area is given by the functionp(t) = 300,000e^-0.09t+(t)/2 f or 0 _< t _< 10 Find
    1. answers icon 0 answers
  2. The present value of a building in the downtown area is given by the functionp(t) = 300,000e^-0.09t+(t)/2 f or 0 _< t _< 10 Find
    1. answers icon 0 answers
more similar questions