Exponential Functions
ICMB200 Business Mathematics
Name Student I.D. Section
1. Graph each function.
(a) y = 3x+2 (b) y = 3x − 2 (c) y = 3−x
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2. Graph each function.
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(a) y = 2(x−1) (b) y = 3x−1 − 1 (c) y = 12 (2x/2 )
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3. The projected population of a city is given by P = 125, 000(1.11)t/20 , where t is the
number of years after 1995. What is the projected population in 2015?
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4. For a certain city, the population P grows at the rate of 1.5%. The formula P =
1, 527, 000(1.015)t gives the population t years after 1998. Find the population in (a)
1999 and (b) 2000.
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5. A radioactive element is such that N grams remain after t hours, where
N = 12e−0.031t .
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(a) How many grams are initially present? To the nearest tenth of a gram, how many
grams remain after (b) 10 hours? (c) 44 hours? (d) Based on your answer to part (c),
what is your estimate of the half-life of this element?
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6. At a certain time, there are 75 milligrams of a radioactive substance. The substance
decays so that after t years the number of milligrams present, N , is given by
N = 75e−0.045t .
How many milligrams are present after 10 years? Give your answer to the nearest
milligram.
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