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Solve the following problems
dealing with exponential functions.
You may want to have your graphing calculator handy.
(Each solution method shown is but one possible approach to the
answer.)
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1. |
Diego decided to invest his $500 tax refund
rather than spending it. He found a bank that would pay him
4% interest, compounded quarterly. If he deposits the
entire $500 and does not deposit or withdraw any other
amount, how long will it take him to double his money in the
account?
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2. |
The half-life of carbon-14 is known to be
5720 years. Doctor Frankenstein has 300 grams
of carbon-14 in his experimental laboratory. If
untouched, how many of the 300 grams will remain after 1200
years? |
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3. |
Your brother tells you a
secret. You see no harm in telling two friends.
After this second "passing" of the secret, 4 people now know
the secret (your brother, you and two friends). If
each of these friends now tells two new people, after the
third "passing" of the secret, eight people will know.
If this pattern of spreading the secret continues, how many
people will know the secret after 10 such "passings"? |
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4. |
The radioactive element
polonium-210 has a half-life of 138 days. If you have
100 micrograms of polonium-210, how much will remain after
60 days? |
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5. |
The number of wolves in the
wild in the northern section of the Cataragas county is
decreasing at the rate of 3.5% per year. Your
environmental studies class as counted 80 wolves in the
area. After how many years will this population of 80
wolves drop below 15 wolves, if this rate of decrease
continues? |
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