Question
An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest 10th of a gram?
Answer
4.6
(310 Votes)
Tommy
Professional · Tutor for 6 years
Answer
### 18.3 grams
Explanation
## Step 1: Identify the decay rate per minute### The element decays by
per minute, which means the remaining amount is
per minute, or
times the previous amount.## Step 2: Determine the decay formula### The remaining mass \( m(t) \) after
minutes can be modelled by the formula \( m(t) = m_0 \times (decay\,factor)^t \), where
is the initial mass and the decay factor is
.## Step 3: Calculate the remaining mass after 10 minutes### Initial mass
grams, decay factor =
, and
:
## Step 4: Compute the numerical value### Using a calculator or computation tool: