Hi All,
I have been spending more than an hour on this question and it is driving me nuts.
9. A theory of investment has used a function W defined for all T > 0 by:
. . . . .\(\displaystyle \displaystyle W(T)\, =\, \dfrac{K}{T}\, \int_0^T\, e^{-\varrho t}\, dt\)
...where K and \(\displaystyle \varrho\) are positive constants.
Evaluate the integral. Then prove that W(T) takes values on the interval (0, K) and is strictly decreasing. (Hint: Problem 6.11.11.)
So far I can only prove that the equation is strictly increasing instead of what the question is asking for (to prove it is decreasing).
I have been spending more than an hour on this question and it is driving me nuts.
9. A theory of investment has used a function W defined for all T > 0 by:
. . . . .\(\displaystyle \displaystyle W(T)\, =\, \dfrac{K}{T}\, \int_0^T\, e^{-\varrho t}\, dt\)
...where K and \(\displaystyle \varrho\) are positive constants.
Evaluate the integral. Then prove that W(T) takes values on the interval (0, K) and is strictly decreasing. (Hint: Problem 6.11.11.)
So far I can only prove that the equation is strictly increasing instead of what the question is asking for (to prove it is decreasing).
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