Question

at the moment a certain medicine is injected, its concentration in the bloodstream is 120 milligrams per liter. from that moment forward, the medicines concentration drops by 30% each hour. write a function that gives the medicines concentration in milligrams per liter, c(t), t hours after the medicine was injected. c(t) =

Explanation:

Step1: Identify remaining concentration rate

Since concentration drops by 30% each hour, the remaining concentration is $100\% - 30\% = 70\% = 0.7$.

Step2: Set up exponential decay function

The initial concentration is 120 mg/L, and the remaining concentration multiplies by 0.7 each hour. For $t$ hours, the function follows the exponential decay form $C(t) = \text{Initial Value} \times (\text{Decay Rate})^t$.
$C(t) = 120 \times (0.7)^t$

Answer:

$C(t) = 120(0.7)^t$