Half-life question?

If Grandma’s cookies have a half life of 2 hours and she bakes 3 dozen cookies, how many hours will pass until only two cookies remain uneaten? Round your answer to the nearest minute.

Is it 8 hours and 22 minutes?

1 Answer
Jan 18, 2018

88h2020min

Explanation:

y(t) = a*(1/2)^(0.5t)y(t)=a(12)0.5t

(where tt is in hours)

e.g. y(2) = (1/2)^1 * 36 = 1/2 * 36y(2)=(12)136=1236

(this is the number after the first half-life.)

33 dozen = 36=36

a = 36a=36

if y(t) = 2y(t)=2:

2 = a*(1/2)^(0.5t)2=a(12)0.5t

2 = 36*(1/2)^(0.5t)2=36(12)0.5t

(1/2)^(0.5t) = 1/18(12)0.5t=118

0.5t = log_(1/2)(1/18)0.5t=log12(118)

0.5t = 4.170.5t=4.17

t = 8.339..t=8.339..

t = 8.339t=8.339h = 8=8h 2020min

(this answer is very close to 88h 2222 min, so you may have rounded differently, but used the right method.)