It is estimated that t weeks from now, the average price of a gallon of milk will be increasing at the rate of p ′ (t)= t/(t^2 +18) If the average price of a gallon of milk is currently $1.85, what will the average price of a gallon of milk be 12 weeks from now?

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Answer:

$1.92

Step-by-step explanation:

[tex]p(12) = \frac{12}{ {12}^{2} + 18 } \\ = \frac{12}{162} = 0.074[/tex]

[tex]1.85 + 0.074 = 1.924 = 1.92[/tex]

The Average price of milk after 12 weeks is $ 1.924.

The average price of a gallon of milk will be increasing with rate of p(t).

                      [tex]p(t)=\frac{t}{t^{2}+18 }[/tex]

Given that, the current average price of milk is $ 1.85.

To find average price after 12 weeks, substitute t = 12 in above equation

                        [tex]p(12)=\frac{12}{(12^{2}+18 )} =\frac{12}{162}=0.074[/tex]

Average price of milk after 12 weeks is, [tex]=0.074+1.85=1.924[/tex]

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