Question

A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how much caffeine will remain in the body after 3 hours?

Write the exponential function and solve.
a.
4072-06-01-04-00_files/i0260000.jpg; 184 mg
b.
4072-06-01-04-00_files/i0260001.jpg; about 346 mg
c.
4072-06-01-04-00_files/i0260002.jpg; less than 1 mg
d.
4072-06-01-04-00_files/i0260003.jpg; about 92 mg

Answer 1

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y(t) = a*e^(kt)
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now:
130 mg
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one hour from intake:
130 * (1 - 0.11) = 115.7 mg
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y(1) = 115.7 = 130*e^(k(1))
115.7 = 130*e^k
115.7/130 = e^k
ln( 115.7/130 ) = ln( e^k )
ln( 115.7/130 ) = k
k = -0.1165338

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three hours from intake:
y(3) = 130*e^(3k)
y(3) = 91.64597
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answer:
three hours after drinking a cup of coffee, 91.6 mg of caffeine will remain in the body