If 8 g of radioactive substance are present initially and 9 yr later only 4.0 remain, how much of the substance, to the nearest tenth of a gram, will be present after 17 yr?

Question

Exponential Growth and Decay

Answer 1

0 years 8 g

9 years 4 g

18 years 2 g half life is 9 years. 18 years is 2 half lives or 1/4 life. 1/4 of 8 = 2 grams

17 years slightly more than 2 g, maybe about 2.1 or 2.2 grams

A=Pe^rt

P=8

t=17

r = rate of decay

.5 = e^9r

take natural logs of both sides and divide by 9

r=ln.5/9

A= 8e^ln.5(17/9) = amount left after 17 years = about 2.160137 g

use a calculator