Page 181 - How To Solve Word Problems In Calculus

After 24 hours, the amount of the substance within the patient’s
body is
ln 2
Q(24) = 10e −( 20 )24
24 ln 2
= 10e − 20
= 10e −1.2ln2
≈ 4.35 mg

Since 2 mg are found in the pancreas, 2.35 mg (4.35 mg − 2 mg) are
in the remainder of the patient’s body.

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5. The ratio r (t)of Cto C present in the papyrus is r (t) = r 0 e −kt .
ln 2 ln 2
Since the half-life is T = 5730 years, k = = .
T 5730
r (t)
= e −kt
r 0

ln 2
− t
0.65 = e 5730

ln 2
− t = ln 0.65
5730

5730
t =−(ln 0.65)
ln 2
t ≈ 3561.1

The papyrus is about 3561 years old.

6. The amount of money P dollars will be worth in t years if
compounded continuously at rate r is

A = Pe rt
In this problem, P = 700, r = 0.08, and t = 3.

A = 700e (0.08)(3)

= 700e 0.24
= 700(1.271249)

= $889.87

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