Question

At the moment a certain medicine is injected, its concentration in the bloodstream is 120 milligrams per liter.

Answer 1

Answer:

$c(t) = 120 [0.7]^{t}$

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

$c(t) = c(0) [1 - \frac{30}{100}]^{t}$

⇒ $c(t) = c(0) [1 - 0.3]^{t}$ 

⇒$c(t) = 120 [0.7]^{t}$ . (Answer)

Answer 2

Answer:

c(t) = $(\frac{70}{100} )^{t} times 120$

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, $\frac{70}{100} times 120$ milligrams per liter.

After 2 hour, the quantity will be $\frac{70}{100} times \frac{70}{100} times120$ = $\frac{70}{100} ^{2} times120$.

Hence, after t hours the  concentration of the medicine can be represented as, c(t) = $(\frac{70}{100} )^{t} times 120$.