a sample of a substance contains 129 grams of an element with a half-life of 7 months. which equation can be…

a sample of a substance contains 129 grams of an element with a half-life of 7 months. which equation can be used to determine how much, $y$, in grams, of the element is remaining after $t$ months?\na. $y = 129\\left(\\frac{7}{2}\\right)^t$\nb. $y = \\frac{129}{7}\\left(\\frac{1}{2}\\right)^t$\nc. $y = 129\\left(\\frac{1}{2}\\right)^{7t}$\nd. $y = 129\\left(\\frac{1}{2}\\right)^\\frac{t}{7}$

a sample of a substance contains 129 grams of an element with a half-life of 7 months. which equation can be used to determine how much, $y$, in grams, of the element is remaining after $t$ months?\na. $y = 129\\left(\\frac{7}{2}\\right)^t$\nb. $y = \\frac{129}{7}\\left(\\frac{1}{2}\\right)^t$\nc. $y = 129\\left(\\frac{1}{2}\\right)^{7t}$\nd. $y = 129\\left(\\frac{1}{2}\\right)^\\frac{t}{7}$

Answer

Explanation:

Step1: Recall half-life formula

The general formula for exponential decay with half-life is $y = a\left(\frac{1}{2}\right)^{\frac{t}{h}}$, where $a$ is the initial amount, $t$ is time, and $h$ is the half-life.

Step2: Substitute given values

Here, $a = 129$ grams, $h = 7$ months. Substitute into the formula: $y = 129\left(\frac{1}{2}\right)^{\frac{t}{7}}$

Step3: Match to options

Compare the derived formula to the provided choices.

Answer:

D. $y = 129\left(\frac{1}{2}\right)^{\frac{t}{7}}$