Question

one of the main contaminants of a nuclear accident, such as that at chernobyl, is strontium - 90, which decays exponentially at a rate of approximately 2.4% per year. (a) write the percent of strontium - 90 remaining, p, as a function of years, t, since the nuclear accident. hint: 100% of the contaminant remains at t = 0. p(t)=100·0.976^t

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - decay function is $P(t)=P_0(1 - r)^t$, where $P_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time.

Step2: Identify the initial amount and decay rate

We are given that initially ($t = 0$), $P_0=100$ (since 100% of the contaminant remains at $t = 0$) and the rate of decay $r = 0.024$ (because 2.4%=0.024).

Step3: Substitute values into the formula

Substituting $P_0 = 100$ and $r=0.024$ into the formula $P(t)=P_0(1 - r)^t$, we get $P(t)=100\times(1 - 0.024)^t=100\times0.976^t$. The original answer is correct. There may be a marking error.

Answer:

$P(t)=100\times0.976^t$