+0

# creating a rational exponent equation??

0
135
4

household smoke detectors contain 200 ug of a radioactive element that has a half-life of 432 years. to the nearest 10 ug, how much of this element will remain in a smoke detector after 20 years?

Guest Jul 20, 2017
Sort:

#1
0

R =200 x 2^-(20/432)

R =200 x 2^-(1/21.6)

R =200 x 0.96841927.....

R =193.684 ug remains after 20 years.

Guest Jul 20, 2017
edited by Guest  Jul 20, 2017
#3
+1

why a negative exponent? just wondering :)

Guest Jul 21, 2017
#4
+91229
0

Because the quantity is decreasing over time.

Melody  Jul 21, 2017
#2
+26357
+1

N(t) = N(0)*e-kt  where  k = ln(2)/tau   tau is half-life.

k = ln(2)/432 ≈ 1.605*10-3 per year

N(20) = 200*e-1.605*10^(-3)*20 ug ≈ 193.7 ug = 190 ug to the nearest 10 ug.

Alan  Jul 20, 2017
edited by Alan  Jul 20, 2017

### 21 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details