March 27
Name:
1. (3 pts) A new company’s revenues are growing 21% per year. The doubling time for
its revenue is
log10 2
a.
years
log10 (1 + 0.21)
2. (3 pts) log10 (7.1 × 106 ) is between
a. 5 and 6.
b. 6 and 7.
c. 7 and 8.
3. (3 pts) Which of the following is an example of exponential decay?
a. The population of a community is falling by 0.5% people per year.
Tip: Again, look to see if the quantity is a percentage or not. Exponential growth
or decay will be accompanied by a percentage rate.
4. (3 pts) The value of your house is increasing by 1.2% per year. If it is worth $300,000
today, what will it be worth seven years from now?
$300, 000 × (1 + 0.012)7 = $36, 125.60
You may have built a table, finding 1.2% of the end of year balance.
5. (3 pts) Prices are rising at a rate of 4.4% per month. What is the approximate
doubling time? For an item that costs $25 today, how much will it cost in a year?
Rule of 70: Tdouble ≈ 70/4.4 = 15.9 months.
Then 1 year = 12 months and
$25 × 2(12/15.9) = $42.18
6. (3 pts) The half-life of a drug in the bloodstream is 8 hours. What fraction of the
original drug dose remains in 24 hours? The original dosage is 80 milligrams. How
much (in milligrams) of the dose remains in 24 hours?
(1/2) × (1/2) × (1/2) = 0.125 or 12.5%
In class, we got this using (1/2)(24/8) = 0.125.
There will be 12.5% of 80 mgs in 24 hrs. This is 10 mg since (0.125 × 80 = 10).
7. (3 pts) Hyperinflation is driving up prices at a rate of 50% per month. What is the
exact doubling time? For an item that costs $40 today, what will the price be in 9
months?
log10 2
Using r = 0.50, Tdouble =
= 1.71 months.
log10 (1 + 0.5)
$40 × 2(9/1.71) = $1, 536.13
8. Extra Credit (1 pt) Why shouldn’t the Rule of 70 be used for an inflation rate of
50% per month?
The Rule of 70 is good approximation for doubling time for percents that are small
and under 15%. 50% is much larger than 15%.