Question

An element with mass 290 grams decays by 13.2% per minute. How much of the

element is remaining after 14 minutes, to the nearest 10th of a gram?​

Answer 1

40.0 grams

Explanation:

An exponential decay function is

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

where, a is initial value, t is time and r is decay rate.

It is given that element with mass 290 grams decays by 13.2% per minute.

Initial value = 290

Decay rate = 13.2% = 0.132

Substitute a=290 and r=0.132 in equation (1).

`y=290(1-0.132)^t`

`y=290(0.868)^t`

Substitute t=14 to find the amount of element remaining after 14 minutes.

`y=290(0.868)^(14)`

`y=39.9644785`

Round the solution to the nearest tenth.

`y\approx 40.0`

Therefore, element with mass 40.0 grams is remaining after 14 minutes.