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 1

Decay

$$m(t)=m(0)e^{kt}$$

Given $m(0)=730\ g$

$$m(1)=m(0)e^{k(1)}=(1-0.288)m(0)$$

$$k=\ln0.712$$

$$m(t)=730e^{(\ln0.712)t}=730(0.712)^t$$

$$m(10)=730(0.712)^{10}$$

$$m(10)=24.4\ g$$