Page 167 - How To Solve Word Problems In Calculus

y(10) = 100e −10 k

75 = 100e −10 k
3
= e −10 k
4

3
−10k = ln
4
4
10k = ln
3

1 4
k = ln ← k is a positive number
10 3

The function y(t) can now be determined.

4
1 ln )t
y(t) = 100e −( 10 3
t ln 4
= 100e − 10 3
= 100(e ln 4 3 ) − 10 t
t
−
4 10
= 100
3
To solve the problem, let t = 20.

4
−2
y(20) = 100
3

2
3
= 100
4
9
= 100 ·
16

= 56.25 mg

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