Pretzels are given away for free at a local store. The tray is constantly replenished as people take the pretzels.The number of pretzels in the tray is given by the function P(t) = 20 + t^2 − 8cosπt , where t is measured in minutes. When t = 1 minute, find the average rate of change of pretzels in the tray over the next 30 seconds.

Answer:

The answer is "[tex]-13.5 \ / minute \\\\[/tex]"

Step-by-step explanation:

The average rate to the changes of pretzels form [tex]t= 1 \ minutes[/tex] to [tex]t=1.5 \ minutes[/tex] will be:

[tex]=\frac{P(1.5)-p(1)}{1.5-1}\\\\=\frac{(20+(1.5)^2- 8 \cos \pi (1.5))-(20+1^2 -8 \cos \pi)}{0.5}\\\\=\frac{22.25-29}{0.5}\\\\=\frac{-675}{50}\\\\=-13.5 \ / minute \\\\[/tex]

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