The function displaystyle{left({9}{h}right)}={8}{e}^{{-{0.4}{h}}} can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be resent in 7 years?

The function displaystyle{left({9}{h}right)}={8}{e}^{{-{0.4}{h}}} can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be resent in 7 years?

Question
Decimals
asked 2020-10-28
The function \(\displaystyle{\left({9}{h}\right)}={8}{e}^{{-{0.4}{h}}}\) can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be resent in 7 years?

Answers (1)

2020-10-29
Step 1
Given that the function \(\displaystyle{D}{\left({h}\right)}={8}{e}^{{-{0.4}{h}}}\) represents the miligrams D of a certain drug in a patient's bloodstream after h hours.
Substitute \(\displaystyle{h}={7}\in{D}{\left({h}\right)}={8}{e}^{{-{0.4}{h}}}.\)
\(\displaystyle{D}{\left({7}\right)}={8}{e}^{{-{0.4}{\left({7}\right)}}}\)
\(\displaystyle={8}{e}^{{-{2.8}}}\)
\(\displaystyle\approx{0.49}\)
Step 2
Hence, 0.49mg amount of drug will be present in 7 hours.
Note that for 7 hours, the amount of drug present in bloodstream is 0.49, which means that in 7 years it will be 0.
0

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