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anzhelika [568]
3 years ago
12

The average price of a ticket to a baseball game can be approximated by ​p(x)equals0.03 x squared plus 0.42 x plus 9.63​, where

x is the number of years after 1991 and​ p(x) is in dollars. ​a) Find ​p(3​). ​b) Find ​p(13​). ​c) Find ​p(13​)minus​p(3​). ​d) Find StartFraction p (13 )minus p (3 )Over 13 minus 3 EndFraction ​, and interpret this result.
Mathematics
1 answer:
irina [24]3 years ago
8 0

Answer:

a) We want to find p(3) and if we replace x=3 into p(x) we got:

p(3) = 0.03*(3)^2 +0.42*3 +9.63 = 11.16

b) We want to find p(13) and if we replace x=13 into p(x) we got:

p(13) = 0.03*(13)^2 +0.42*13 +9.63 = 20.16

c) p(13)-p(3) = [0.03*(13)^2 +0.42*13 +9.63]-[0.03*(3)^2 +0.42*3 +9.63] = 20.16-11.16 = 9

d)  \frac{p(13)-p(3)}{13-3}

If we use the result from part c we have:

\frac{p(13)-p(3)}{13-3}= \frac{9}{10}= 0.9

And the interpretation for this case would be:

It represents the average rate of change in price from 1996 to 2006.

Step-by-step explanation:

For this case we have the following function given:

p(x) = 0.03 x^2 +0.42 x +9.63

Part a

We want to find p(3) and if we replace x=3 into p(x) we got:

p(3) = 0.03*(3)^2 +0.42*3 +9.63 = 11.16

Part b

We want to find p(13) and if we replace x=13 into p(x) we got:

p(13) = 0.03*(13)^2 +0.42*13 +9.63 = 20.16

Part c

For this case we want to find p(13) -p(3) and we have from the results of part a and b this:

p(13)-p(3) = [0.03*(13)^2 +0.42*13 +9.63]-[0.03*(3)^2 +0.42*3 +9.63] = 20.16-11.16 = 9

Part d

For this case we want to find:

\frac{p(13)-p(3)}{13-3}

If we use the result from part c we have:

\frac{p(13)-p(3)}{13-3}= \frac{9}{10}= 0.9

And the interpretation for this case would be:

It represents the average rate of change in price from 1996 to 2006.

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