Determine when the taste quality will be one half of its original value.

Question

Twinkies on the shelf of a convenience store lose their fresh tastiness over time. We say that the taste quality is  when the Twinkies are first put on the shelf at the store, and that the quality of tastiness declines according to the function  ( in days). 

The taste quality will be one half its original value after ___days.

Answer 1

in one day Q = .85

in two days Q = .85^2 = .7225

in three days Q = .85^3 > 1/2

in 4 days .85^4 > 1/2

in 5 days .85^5 < 1/2

in t days Q = .85^t = .5 = 1/2

t = between 4 and 5 days

t= about 4 days 6 hours 21 minutes 38 seconds

.5 = .85^t

log.5 = tlog.85

t = log.5/log.85 = about 4.26...days