the half - life of a certain substance is about 4 hours. the graph shows the decay of a 50 gram sample of…

Answer:

$y = 50(0.85)^t$

Explanation:

Step1: Recall decay - formula

The general formula for exponential decay is $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. The initial amount $a = 50$ grams.

Step2: Use half - life information

The half - life is 4 hours. Let's find the decay factor for 1 hour. If the half - life is 4 hours, after 4 hours, the amount is halved. Let the decay factor per hour be $x$. So, $50x^4=25$. Then $x^4=\frac{25}{50}=0.5$. Solving for $x$, we get $x = 0.5^{\frac{1}{4}}\approx0.84$. Among the given options, the function with $a = 50$ and a decay factor close to 0.84 is $y = 50(0.85)^t$.