times per year the interest is assessed. Since in our example, the interest is
compounded per year, n = 1, this gives us:
Note: When you do this on the calculator, make sure you evaluate the
exponent part first, and then multiply by the 2,500 (using parentheses on a
scientific calculator works best).
EXPONENTIAL DECAY
Just as things can grow very quickly, they can also shrink exponentially; this is
called “decay.” For example, a stock price that starts at $50 per share may drop
by a certain percentage each year. If a $50 stock declines 20% per year, you can
calculate its final value after 3 years, just as you calculated the growth of an
investment over 3 years. You’ll use the exact same formula as growth, with one
important difference—the plus sign before the r/n part becomes a minus sign:
Exchange Rates
Problems involving exchange rates are also just ratio problems in disguise.
A student traveling in Moscow bought a sweater for 175 rubles. When
she checked her bank account, she realized that this was equivalent to
$65. What was the exchange rate of rubles per dollar, rounded to the
nearest tenth?
A) .8 B) 1.1 C) 1.7 D) 2.7To figure out a rate of exchange, set up an equivalency:
Cross multiply to find out that there are 2.69 rubles per dollar, which rounds to
2.7, or D.