Difference between revisions of "009B Sample Midterm 3, Problem 4"

Revision as of 08:03, 7 February 2017

The rate of reaction to a drug is given by:

r'(t)=2t^{2}e^{-t}

where $t$ is the number of hours since the drug was administered.

Find the total reaction to the drug from $t=1$ to $t=6.$

Foundations:
If we calculate $\int _{a}^{b}r'(t)~dt,$ what are we calculating?
We are calculating $r(b)-r(a).$ This is the total reaction to the
drug from $t=a$ to $t=b.$

Solution:

Final Answer:

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 !Foundations: &nbsp;
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+|If we calculate <math style="vertical-align: -14px">\int_a^b r'(t)~dt,</math> what are we calculating?
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+::We are calculating <math style="vertical-align: -5px">r(b)-r(a).</math> This is the total reaction to the
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+::drug from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
 |}