Question 1

1 (25pts) What nominal interest rate is needed for $1200 to grow to $2000 in 8 years if the compounding is monthly? Round your answer to two decimal places AFTER you have converted the answer to a percent. Do not round anything at all before this final point.

Solution $$A = P(1+\frac{r}{m})^{mn}$$ $$2000 = 1200(1+\frac{r}{12})^{12*8}$$ $$ (\frac{2000}{1200})^{\frac{1}{96}} = 1 + \frac{r}{12}$$ $$(\frac{2000}{1200})^{\frac{1}{96}}-1 = \frac{r}{12}$$ $$ 12[(\frac{2000}{1200})^{\frac{1}{96}}-1] = r $$ $$ r = 6.042%$$

Question 2

$$f(x) = e^{x^{3}-2x+8}$$

$$f^{'}(x) = (3x^{2}-2)e^{x^{3}-2x+8}$$

Question 3

$$f^{''}(x) = (3x^{2}-2)^{2}e^{x^{3}-2x+8} + 6xe^{x^{3}-2x+8}$$

Question 4

$$ f(x) = \log(x^{2}+17x-5)$$ $$ f^{'}(x) = \frac{2x+17}{x^{2}+17x-5}$$