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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?

Respuesta :

Answer:

The graph is shown below.

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

Step-by-step explanation:

Given:

Initial value of the taste is, [tex]Q_0=1[/tex]

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

[tex]Q(t)=Q_0(0.85)^t\\Q(t)=1(0.85)^t[/tex]

Now, when the taste reduces to half, [tex]Q=0.5[/tex]

Therefore,

[tex]0.5=1(0.85)^t[/tex]

Taking natural log on both the sides, we get:

[tex]\ln(0.5)=\ln(0.85)^t\\\ln(0.5)=t\ln(0.85)\\t=\frac{ln(0.5)}{\ln(0.85)}=4.265\ s[/tex]

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

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