Question

question
a radioactive compound with mass 470 grams decays at a rate of 3% per hour. which equation represents how many grams of the compound will remain after 6 hours?
answer
\\( c = 470(0.03)^6 \\)
\\( c = 470(0.7)^6 \\)
\\( c = 470(1 + 0.03)^6 \\)
\\( c = 470(1 - 0.03)^6 \\)

Explanation:

Step1: Identify decay formula

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

Step2: Plug in given values

Here, $P=470$, $r=0.03$, $t=6$. Substitute into formula: $C = 470(1 - 0.03)^6$

Answer:

$C = 470(1 - 0.03)^6$