You invest $1000 at 6% compound interest a year. How long does it take until your investment is worth $2000?
a. Based on what you know about exponential regression, explain why the answer is the value of x for which 1000(1.06)x = 2000.
b. Using the property of logarithms that log(ax) = x log(a), show that the answer x satisfies x[log(1.06)] = log(2), or x = log(2)/log(1.06) = 12.
c. The rule of 72 says that if you divide 72 by the interest rate, you will find approximately how long it takes your money to double. According to this rule, about how long (in years) does it take your money to double at an interest rate of
(i) 1% and
(ii) 18%?