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WILL GIVE BRAINLIEST The number of milligrams of a certain drug that is in a patient's bloodstream h hours after the drug is injected is given by the following function.
When the number of milligrams reaches 6 , the drug is to be injected again. How much time is needed between injections?

Round your answer to the nearest tenth, and do not round any intermediate computations.

WILL GIVE BRAINLIEST The number of milligrams of a certain drug that is in a patients bloodstream h hours after the drug is injected is given by the following f class=

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Hrishii

Answer:

3.6 hours

Step-by-step explanation:

[tex]D(h) = 25 {e}^{ - 0.4h} \\ \\ \implies \: 6 = 25 {e}^{ - 0.4h} \\ \\ \implies \: \frac{6}{25} = {e}^{ - 0.4h} \\ \\ \implies \: 0.24 = {e}^{ - 0.4h} \\ Taking\: natural\: log\:both\: sides \\ In(0.24) = - 0.4h \: In\: e \\ \\ \implies \: -1.42711635564 = - 0.4h\\(\because\:In\:e=1) \\ \\ \implies \: h= \frac{-1.42711635564}{ - 0.4} \\ \\ \implies \: h = 3.5677908891 \\ \\ \implies \: h = 3.6 \: hours[/tex]

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