Question

Suppose a (the word 'a' means starting amount is 1) radioactive substance decays at a rate of 5% per hour, what percent of the substance is left after 10 hours? (make sure you convert your answer from decimal to percent and round to the nearest whole percent)

Answer 1

The percentage of the substance is left after 10 hours is 60%.

Explanation:

The expression representing the amount left after a certain period of decay is:

`y=a(1-r)^(t)`

Here,

y = final amount

a = initial amount

r = decay rate

t = time taken

It is provided that:

a = 1

r = 5% / hour

t = 10 hours

Compute the percentage of the substance is left after 10 hours as follows:

`y=a(1-r)^(t)`

`=1* (1-0.05)^(10)\\\\=0.95^(10)\\\\=0.598737\\\\\approx 0.60`

The percentage is: 0.60 × 100 = 60%.

Thus, the percentage of the substance is left after 10 hours is 60%.