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 decay factor

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

Step3: Compute exponent term

Calculate $0.732^{18}$:
$0.732^{18} \approx 0.002704$

Step4: Find remaining mass

Multiply initial mass by the result:
$A = 820 \times 0.002704$

Answer:

2.2 grams