Question

Please show a step by step on how to solve.

Twinkies on the shelf of a convenience store lose their fresh tastiness over time. We say that the taste quality is 1 when the Twinkies are first put on the shelf at the store, and that the quality of tastiness declines according to the function Q(t) = .85' (t in days). Determine when the taste quality will be one half of its original value. The taste quality will be one half its original value after days. Enter your answer as an integer or decimal number. Examples: 3.-4.5.5172 Enter DNE for Does Not Exist, oo for Infinity

Answer 1

Q(t) = 0.85^t

When Q(t) = 1/2,

(1/2) = 0.85^t

Taking ln both sides

ln(1/2) = t*ln(0.85) = t*(-0.162)

-0.693 = t*(-0.162)

t = -0.693/-0.162 = 4.278