An element with mass 130 grams decays by 22% per minute. How much of the element is remaining after 7 minutes, to the nearest 10th of a gram?

Question

alegebra

Answer 1

130 grams decays at 22% per minute

how much is left after 7 minutes

t=0, 130 g

t=1 130-.22(130) = 130-28.6 = 101.4 grams after one minute

t=2 101.4-.22(101.4) = 101.4-22.308 = 79.092 grams after two minutes

t=3 A = 79.092-.22(79.092) = 61.692

t=4 A= 61.692 -.22(61.692) = 48.12

t=5 A = 48.12 -.22(48.12) = 37.534

t=6, A = 37.534 -.22(37.534) = 29.277

t=7 A = 29.277 -.22(29.277) = 22.84 grams after 7 minutes

as t approaches infinity, A approaches but never reaches zero

that above calculation involves rounding errors,

the decay is continuous, so use the continuous compounding/decay formula:

A = Pe^rt = 130e^.-22t where e=an irrational number = about 2.718281828...

A= 130e^.-22(7)= 130e^-1.54 = about 130/(2.718^1.54)

A= about 27.9 grams after 7 minutes