Question

# 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?

Decimals
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?

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.