a radioactive compound with mass 430 grams decays at a rate of 28% per hour. which equation represents how…

a radioactive compound with mass 430 grams decays at a rate of 28% per hour. which equation represents how many grams of the compound will remain after 5 hours? answer \\( c = 430(1 + 0.28)^5 \\) \\( c = 430(1 - 0.28)(1 - 0.28)(1 - 0.28) \\) \\( c = 430(0.72)^5 \\) \\( c = 430(1.28)^5 \\)

a radioactive compound with mass 430 grams decays at a rate of 28% per hour. which equation represents how many grams of the compound will remain after 5 hours? answer \\( c = 430(1 + 0.28)^5 \\) \\( c = 430(1 - 0.28)(1 - 0.28)(1 - 0.28) \\) \\( c = 430(0.72)^5 \\) \\( c = 430(1.28)^5 \\)

Answer

Explanation:

Step1: Identify decay formula

The general exponential decay formula is $C = P(1 - r)^t$, where $P$ is initial mass, $r$ is decay rate, $t$ is time.

Step2: Substitute given values

$P=430$, $r=0.28$, so $1-r=0.72$, $t=5$. Substitute to get $C = 430(0.72)^5$.

Step3: Eliminate incorrect options

Options with $1+0.28$ or $1.28$ are growth formulas, wrong. The option with 3 factors of $(1-0.28)$ uses $t=3$, not 5, wrong.

Answer:

$C = 430(0.72)^5$