Quiz 5 answer key
Math 1030-005 (Fall 2014)
1. The balance owed on your credit card doubles from $2000 to $4000 in 6 months. If your balance
is growing exponentially, how much longer will it be until it reaches $8000? (3 points)
Ans: Another 6 months.
2. At 11 : 00 you place a single bacterium in a bottle, and at 11 : 01 it divides into 2 bacteria, which at
11 : 02 divide into 4 bacteria, and so on. How many bacteria will be in the bottle at 11 : 25? (3 points)
Ans: 225 bacteria.
3. Cobalt-56 has a half-life of 77 days. If you start with kilogram of cobalt-56, how much will it
remain after 77 days? (1 point) 30 days? (2 points)
Ans: (1) 0.5 kg. (2) (1/2)30/77 ≈ 0.763 kg
4. The price of some product is falling exponentially at a rate of 25% every month. (1) Which formula
can we use on this product, doubling time or half-life? (1 point) (2) Why it is not appropriate to
use approximate (doubling time or half-life) formulas for this problem? (1 point) (3) Use the exact
formula to calculate the doubling time or half-life for this product. (1 point)
Ans: (1) half-life, because this is an exponentially decay model. (2) To use approximate half-life
or doubling time formula, p should be less than or equal to 15. Here we have p = 25. (3) The exact
10 2
≈ 2.41 (month).
half-life is − log log(1−0.25)
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