Question

a radioactive compound with mass 100 grams decays at a rate of 19% per hour. which equation represents how many grams of the compound will remain after 3 hours?
answer
c = 100(1 - 0.19)
c = 100(1.19)^3
c = 100(1 + 0.19)^3
c = 100(1 - 0.19)(1 - 0.19)(1 - 0.19)

Explanation:

Step1: Identify decay formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time.

Step2: Substitute given values

Here, $P = 100$ grams, $r=0.19$ (19% expressed as a decimal), and $t = 3$ hours.
The amount $C$ remaining after 3 hours is $C=100(1 - 0.19)^3$, which is equivalent to $C = 100(1 - 0.19)(1 - 0.19)(1 - 0.19)$.

Answer:

$C = 100(1 - 0.19)(1 - 0.19)(1 - 0.19)$