An element with mass 570 grams decays by per minute. How
much of the element is remaining after 14 minutes, to the nearest 10 th of
a gram?

Question

An element with mass 570 grams decays by $$ 26.9 \% $$ per minute. How much of the element is remaining after 14 minutes, to the nearest 10 th of a gram?

UpStudy AI · Accepted Answer

The decay rate per minute is $$26.9\%$$, meaning that each minute the element retains

$$
100\% - 26.9\% = 73.1\%
$$

of its mass. In decimal form, the retention factor per minute is

$$
0.731.
$$

Let $$ A_0 = 570 $$ grams be the initial mass, and let $$ A(t) $$ be the amount remaining after $$ t $$ minutes. The decay process is modeled by

$$
A(t) = A_0 \times (0.731)^t.
$$

For $$ t = 14 $$ minutes:

$$
A(14) = 570 \times (0.731)^{14}.
$$

To compute $$ (0.731)^{14} $$, we can use logarithms:

$$
\ln((0.731)^{14}) = 14 \ln(0.731).
$$

Approximating:

$$
\ln(0.731) \approx -0.3133,
$$
$$
14 \ln(0.731) \approx -4.3862,
$$
$$
(0.731)^{14} \approx e^{-4.3862} \approx 0.01243.
$$

Now, multiplying by the initial mass:

$$
A(14) \approx 570 \times 0.01243 \approx 7.086.
$$

Rounded to the nearest tenth of a gram, the remaining mass is

$$
\approx 7.1 \text{ grams}.
$$
After 14 minutes, approximately 7.1 grams of the element remain.

An element with mass 570 grams decays by per minute. How
much of the element is remaining after 14 minutes, to the nearest 10 th of
a gram?

Upstudy AI Solution

Answer

Solution

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An element with mass 570 grams decays by per minute. How much of the element is remaining after 14 minutes, to the nearest 10 th of a gram?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Arithmetic Questions

An element with mass 570 grams decays by per minute. How
much of the element is remaining after 14 minutes, to the nearest 10 th of
a gram?