Selected Applications of Exponentials and Logarithms
1. (Compound interest (once a year)) A principal P is invested at an annual interest rate r, compounded once a year. Suppose the balance after Y years is A. Find the formula of A in terms of
P , r and Y .
2. An investment of $500 is made in an account that compounds interest monthly. After 10 years, the
balance in the account is $1,000. What is the annual interest rate for this account?
3. An investment is made in a trust fund at an annual interest rate of 7.5%, compounded monthly.
How long will it take for the investment to double?
4. (A limit case) You deposit $1 in an account with an annual interest rate of 100%, compounded n
times a year. What’s your balance after one year for the following values of n?
(a) n = 1
(b) n = 100
(c) n = 10000
(d) n = 1000000
5. (Radioactive decay) Radioactive iodine-131 is one of the main pollution in Fukushima nuclear crisis.
Its half-life is 7 days. That is, after 7 days, a given amount of radioactive iodine-131 will have
decayed to half the original amount. Suppose 20 grams of iodine-131 have been released. How long
will it take for the radioactive iodine to decay to a level of 1 gram?