a farmer feeds a cow 9,724 milligrams of an antibiotic. every hour, 50% of the drug breaks down in the cows…

Explanation:

Step1: Identify the decay - formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $A_0=9724$ mg, $r = 0.5$, and $t = 6$.

Step2: Substitute the values into the formula

$A=9724\times(1 - 0.5)^6$. First, calculate $(1 - 0.5)^6$. Since $1-0.5 = 0.5$, then $(0.5)^6=0.5\times0.5\times0.5\times0.5\times0.5\times0.5=\frac{1}{64}=0.015625$.

Step3: Calculate the final amount

$A = 9724\times0.015625$. $9724\times0.015625=\frac{9724}{64}=151.9375$. Rounding to the nearest tenth, we get $151.9$.

Answer:

$151.9$