Half Life Word Problem

Question

A superhero is rendered powerless when exposed to 30 or more grams of a certain element. A 600 year old rock that originally contained 500 grams of this element was recently stolen from a rock museum by the superhero's nemesis. The half-life of the element is known to be 150 years.
a) How many grams of the element are still contained in the stolen rock?
b) For how many years can this rock be used by the superhero's nemesis to render the superhero powerless?
a) The stolen rock still contains about
nothing grams of the element.
(Do not round until the final answer. Then round to two decimal places as needed.)
b) The stolen rock can be used to render the superhero powerless for approximately another
nothing years.
(Round to the nearest whole number as needed.)

Answer 1

Fraction remaining = 0.5ⁿ where n = # of half lives that have elapsed.

a)  number of half lives elapsed = 600 yrs/150 yrs = 4

Fraction remaining = 0.5⁴ = 0.0625

grams left = 0.0625 x 500 grams = 31.25 grams (31 grams to 2 significant figures)

 

b)  30 g/500 g = 0.06 fraction remaining

0.06 = 0.5ⁿ

n = 4.059 half lives

4.059 half lives x 150 yrs/half life = 608.9 years = 609 years (rounded to nearest whole number)