Question

an element with mass 820 grams decays by 26.8% per minute. how much of the element is remaining after 18 minutes, to the nearest 10th of a gram?

Explanation:

Step1: Define decay formula

The exponential decay formula is $A = P(1 - r)^t$, where:

• $P = 820$ (initial mass),
• $r = 0.268$ (decay rate per minute),
• $t = 18$ (time in minutes).

Step2: Calculate remaining factor

First compute $1 - r = 1 - 0.268 = 0.732$.

Step3: Compute decay term

Calculate $0.732^{18}$. Using a calculator, $0.732^{18} \approx 0.002024$.

Step4: Find final mass

Multiply initial mass by the decay term: $A = 820 \times 0.002024$.

Answer:

$1.7$ grams