Answered: A lab sample decays exponentially in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A lab sample decays exponentially in such away that the amount of the sample in grams t hours after it was unpacked is modeled by s ( t ) = 200 ( .74 ) t. How much of the sample will be left 10 hours after it was unpacked? Give your answer as a decimal accurate to two places.

Expert Solution

Step 1

Here, sample decay function is $s (t) = 200 {(. 74)}^{t}$

which means that initially sample was 200gm.

After 10 hours sample decay $s (10) = 200 {(. 74)}^{10}$

$= 200 {(. 74)}^{10} = 9.847980$

Sample left after 10 hours =initial sample-sample decay

=200-9.847980

=190.1520

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