An element with a mass of 740 grams decays by 28.4% per minute. To the nearest minute, how long will it be until there are 30 grams of the element remaining?

Question

asked Mar 28, 2021 59.8k views

2 Answers

Nwellcome · Answer 1 · 2021-04-02T22:48:35+0000

Answer:t=9.6 minutes

Explanation:

Given

mass of element is
$A_o=740\ gm$

Decay rate
$r=28.4\%\ \text{per minute}$

and we know

Amount of exponential decay is given by

A=A_o[1-r]^t

Where
$A_0=\text{Initial amount}$

$\text{A=Accumulated amount}$

$\text{r=rate}$

$\text{t=time}$

Substituting values we get

$\Rightarrow 30=740[1-0.284]^t$

$\Rightarrow (30)/(740)=0.716^t$

$\Rightarrow 0.0405=0.716^t$

taking log both sides we get

$\Rightarrow\ \ln (0.0405)=t* \ln (0.716)$

$\Rightarrow t=(\ln (0.0405))/(\ln (0.716))$

$\Rightarrow t=9.598\approx 9.6\ \text{minutes}$