Question

A company estimates that f(x) thousand software games can be sold at the price of $x as given in the table.

x 20 80 100
f(x) 84 120 168

Estimate the number of games that can be sold at:
a) $24
b) $36

Answer 1

@Twis7ed can u help?

Answer 2

You could use linear interpolation in order to find out the slope of the curve if it was a straight line from say x = 20 to x = 80 and then, using the slope of that line estimate that value of f(x).

Answer 3

can you show it how i will do it?

Answer 4

Ok, so you want to get a reasonably good approximation of the slope of the curve at points x = 24 and x = 36. To do this you get the data that is closest to those intervals that would be, in this case, from x = 20 to x = 80. Using that you can figure out that the slope between these two points would be \[\frac{ 120-84 }{ 80-20 }\] which means a slope of 0.6. Using that, just solve for what the value of the function would be at points 24 and 36.
You won't get an exact answer since 0.6 is not the exact slope of the curve in those intervals but you get a decent approximation.

Answer 5

ok

Answer 6

so how would i solve for those values?

Answer 7

Well, you would know the slope between each x-value so you would just multiply the slope (0.6 in this case) by the change in x from 20 to the value you need and add 84.

^Not sure if that explanation makes much sense :P

Answer 8

lol okay thanks

Answer 9

Hey @Twis7ed i tried to multiply 0.6 into x 20 into 84 but i think i idid it wrong so can you show it ? thanks

Answer 10

What did you get as your answer?

Answer 11

80 :/

Answer 12

is that correct?

Answer 13

No, I can't seem to explain it well so I'll just give you a link with an explanation of the process, http://www.asz.ymmf.hu/talata/math/Exercises/ch03_01.pdf go to page 246 on that and it explains how to do it in a similar setting.

Answer 14

ok

Answer 15

so i got L(x) = f(0.6) + f'(0.6) (x - 0.6) is that correct?

Answer 16

like plugging it in

Answer 17

Yes

Answer 18

okay so now i just solve it right?

Answer 19

Yeah, just plug in the values for 24 and 36 and you'll get the answer

Answer 20

plug those values where?

Answer 21

For a) \[L(24) = 80+0.6(24-20)\] and then for b) all you would have to do is change the value for x

Answer 22

I got f(0.6) + f(0) ( x - 0.6) after i solved

Answer 23

ohh ok

Answer 24

so L(36) = 20 + 0.6 (36 - 20) ?

Answer 25

Almost, remember the f(20) is 80 so it would be L(36)=80+0.6(36-20)

Answer 26

ohh ok

Answer 27

okay so then i just solve

Answer 28

Yep :D

Answer 29

thanks :)