Question

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.
Write a function that gives the medicine's concentration in milligrams per liter, c(t), t hours after the
medicine was injected.​

Answer 1

c(t) =
`((70)/(100) )^(t) times 120`

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,
`(70)/(100) times 120` milligrams per liter.

After 2 hour, the quantity will be
`(70)/(100) times (70)/(100) times120` =
`(70)/(100) ^(2) times120`.

Hence, after t hours the concentration of the medicine can be represented as, c(t) =
`((70)/(100) )^(t) times 120`.

Answer 2

`c(t) = 120 [0.7]^(t)`

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 - (30)/(100)]^(t)`

⇒
`c(t) = c(0) [1 - 0.3]^(t)`

⇒
`c(t) = 120 [0.7]^(t)` . (Answer)