Suppose you invested $x in a monthly-compounded fund that grows incrementally at 1% per month (the average performance of the S\&P 500). That is, this month an $x investment is worth x(1+r)0=x(1)=x dollars, next month the investment is worth x(1+r)0+1=x(1+r)=x(1.01), two months from now it is worth x(1+r)2=x(1.01)2, three months it is worth x(1.01)3 dollars, etc. a. How quickly is the investment growing at 7 time periods after the initial $x investment? b. Suppose the initial investment was $100, how fast is it growing after 7 periods invested? c. If, instead, the investment grew exponentially, valued at x0.01t in month t, what would be the monthly rate of change? Hint for " a ": Find the first derivative of the compound interest function, then solve by plugging in t=7. Hint for " b ": Use a calculator for the second part, give your answer rounded up to the second decimal place. Hint for " c ": It's kind of obvious, but think power rule here