Question

twinlakes on the shelf of a covenience store lose their fresh tastines 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 declined according to the function Q(t)=0.85^t. Graph this function on a graphing calculator, and determine when the taste will be half of its original value?

Answer 1

The graph is shown below.

The time to make the taste to half is 4.265 s.

Explanation:

Given:

Initial value of the taste is,
`Q_0=1`

Therefore, the quality of taste over time 't' is given as:

`Q(t)=Q_0(0.85)^t\\Q(t)=1(0.85)^t`

Now, when the taste reduces to half,
`Q=0.5`

Therefore,

`0.5=1(0.85)^t`

Taking natural log on both the sides, we get:

`\ln(0.5)=\ln(0.85)^t\\\ln(0.5)=t\ln(0.85)\\t=(ln(0.5))/(\ln(0.85))=4.265\ s`

Therefore, the time to make the taste to half is 4.265 s.