Question

An element with mass 590 grams decays by 19.5% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

Answer 1

mass of element is 590grams
19.5% of this is 11.505grams
in 1 minute element deacay is 11.505
in 15 minutes it is172.575grams
remaining element is590-172.575 is 417.425gram or 417grams (approx)
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Answer 2

Concept:

• We will have to use exponential law to solve this question

Given:

• Mass of the element = 590g
• Decay rate = 19.5%/min = 0.195/min
• Time = 15 min

Find:

• Find the amount of the element left after 15 minutes in terms of mass

Solution:

In the first minute, 0.195 of 590g decays, so 0.195*590 = 115.05g is consumed.

The mass left after the first minute = 590 -0.195*590 = 590(1-0.195) = 474.95g

So we can say that, after time t, the mass left is

m = 590 (1-0.195)^t

We know that t = 15 minutes

mass left after 15 minutes, m = m = 590 (1-0.195)^15= 22.8g

The mass remaining after 15 minutes is 22.8g.

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