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

Explanation:

Step1: Recall decay - function formula

The general form of an exponential - decay function is $y = a(b)^t$, where $a$ is the initial amount and $b$ is the decay factor. The initial amount of the substance is $a = 50$ grams since we start with a 50 - gram sample.

Step2: Analyze the half - life

The half - life is 4 hours. We can use the fact that when $t = 4$, $y=\frac{a}{2}$. For $a = 50$, when $t = 4$, $y = 25$. Substitute into $y=a(b)^t$: $25=50(b)^4$.

Step3: Solve for the decay factor $b$

Divide both sides of the equation $25 = 50(b)^4$ by 50: $\frac{25}{50}=(b)^4$, so $0.5=(b)^4$. Then $b = 0.5^{\frac{1}{4}}\approx0.84$. Rounding to two decimal places, $b\approx0.85$.

Answer:

$y = 50(0.85)^t$