(Solved): 25. If a sum of \( \$ 1000 \) is deposited into an account that 26. Suppose that the profit (in hun ...

25. If a sum of \( \$ 1000 \) is deposited into an account that 26. Suppose that the profit (in hundreds of dollars) pays \( r \% \) interest compounded semiannually, the balance after 12 years is given by from selling \( x \) units of a product is given by \( A=1000\left(1+\frac{r}{200}\right)^{24} \). Find \( \frac{d A}{d r} \) when \( r=7.5 \). \( P(x)=\frac{x^{2}}{(x-1)^{2}} \). Find the marginal profit when the number of units sold \( x=5 \). (Hint: Use quotient rule) 27. An average student enrolled in a typing class 28. Given the price-supply function. progressed ata rate of \( \frac{d N(t)}{d t}=7 e^{-0 . t 6} \) words per minute \( t \) weeks after enrolling in a 15 -week course. If a student could type 25 words per supply interval \( [40,50] \). minute at the beginning of the course, how many words per minute \( N(t) \) would the student be expected to type tweeks into the course? After completing the course.