Question An element with mass 210 grams decays by 8.3% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram? Answer Attemptiout of 2

Question

Answer 1

### 60.6 grams

Answer 2

## Step 1: Identify the decay formula### The decay of an element can be modeled using the exponential decay formula:

, where

is the mass at time

,

is the initial mass,

is the decay constant, and

is time.## Step 2: Determine the decay constant### The decay rate is given as 8.3% per minute, which means

per minute. This is because

and here

.## Step 3: Apply the formula to find the remaining mass after 15 minutes### Using the formula with

grams,

, and

minutes, we get:

M(15) = 210 \cdot e^{-0.083 \cdot 15}

## Step 4: Calculate the exponent### Calculate the exponent value:

-0.083 \cdot 15 = -1.245

## Step 5: Compute the remaining mass### Substitute the exponent back into the formula and compute:

M(15) = 210 \cdot e^{-1.245} \approx 210 \cdot 0.2887 = 60.627 \text{ grams}

## Step 6: Round the result### Round to the nearest tenth of a gram:

grams.

Question