A certain substance has half-life of 16 hours. A scientist initially has 100 mg of this substance. A(write the exponential that gives the amount of substance in mg, A(t) as a function of t hours B)When will there be 78mg left? C)How much is left after 200 hours?

A certain substance has half-life of 16 hours. A scientist initially has 100 mg of this substance. A(write the exponential that gives the amount of substance in mg, A(t) as a function of t hours B)When will there be 78mg left? C)How much is left after 200 hours?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 2ECP

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Question

Expert Solution

Step 1

The exponential decay formula is:

$A (t) = a \cdot b^{t} . . . (1)$

where t is the time in hours a is the initial amount and A(t) is the amount in mg after t hours.

(A) Now, the half-life is 16 hours means at $t = 16, A (16) = \frac{a}{2}$ . So, (1) will give:

$\frac{a}{2} = a {(b)}^{16} \Rightarrow b^{16} = 2 \Rightarrow b = 2^{\frac{1}{16}} \Rightarrow b = 0.9576$

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