Question

a farmer feeds a cow 9,724 milligrams of an antibiotic. every hour, 50% of the drug breaks down in the cows body. how much will be left in 6 hours? if necessary, round your answer to the nearest tenth. milligrams

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 9724$ milligrams, $r = 0.5$ (since 50% = 0.5), and $t = 6$ hours.

Step2: Substitute the values into the formula

Substitute $P = 9724$, $r = 0.5$, and $t = 6$ into the formula: $A = 9724(1 - 0.5)^6$.

Step3: Simplify the expression

First, calculate $(1 - 0.5)^6 = (0.5)^6 = \frac{1}{64} = 0.015625$. Then, multiply by 9724: $A = 9724 \times 0.015625$.

Step4: Calculate the final amount

$9724 \times 0.015625 = 152.09375$. Rounding to the nearest tenth gives $152.1$.

Answer:

152.1