Answer:
[tex]c(t) = 120 [0.7]^{t} [/tex]
Step-by-step explanation:
At the moment a certain medicine is injected, its concentration in the bloodstream is 120 milligrams per liter.
From that moment forward, the medicine's concentration drops by 30% each hour.
Therefore, the medicine concentration c(t) in mg/liters after t hours will be modeled as
[tex]c(t) = c(0) [1 - \frac{30}{100}]^{t} [/tex]
⇒ [tex]c(t) = c(0) [1 - 0.3]^{t} [/tex]
⇒[tex]c(t) = 120 [0.7]^{t} [/tex] . (Answer)
Answer:
Step-by-step explanation:
The concentration of the medicine reduce 30% for each passing hour.
After one hour, it will reduce 30% of its concentration, that is remaining concentration of the medicine is (100 - 30)% = 70%
After 1 hour, the concentration will be, [tex]\frac{70}{100} times 120[/tex] milligrams per liter.
After 2 hour, the quantity will be [tex]\frac{70}{100} times \frac{70}{100} times120[/tex] = [tex]\frac{70}{100} ^{2} times120[/tex].
Hence, after t hours the concentration of the medicine can be represented as, c(t) = [tex](\frac{70}{100} )^{t} times 120[/tex].
