Question

question
an element with mass 630 grams decays by 18.8% per minute. how much of the element is remaining after 7 minutes, to the nearest 10th of a gram?
answer attempt 1 out of 2
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Explanation:

Step1: Identify decay formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $A_0=630$ grams, $r = 0.188$, and $t = 7$.

Step2: Substitute values

Substitute the values into the formula: $A=630\times(1 - 0.188)^7$.
First, calculate $1-0.188 = 0.812$. Then, find $(0.812)^7$.
$(0.812)^7=0.812\times0.812\times0.812\times0.812\times0.812\times0.812\times0.812\approx0.2117$.

Step3: Calculate final amount

Multiply the result by the initial amount: $A = 630\times0.2117\approx133.4$.

Answer:

$133.4$