Question

A businessman models the number of items (in thousands) that his company sold from 1998 through 2004 as N(x) = -0.1x³ + x² - 3x + 4 and the average price per item (in dollars) as

P(x) = 0.2x + 5, where x represents the number of years since 1998.

Write a polynomial R(x) that can be used to model the total revenue for this company.

Answer 1

I think revenue is the money coming in, which is the number of items sold times the cost per item.

so R(x)= P(x)*N(x)

they probably want you to multiply it out.

Answer 2

So it would be:

R(x) = (0.2x + 5)(-0.1x³ + x² - 3x + 4)

@phi

Answer 3

yes.

Answer 4

Okay! I can do that!

Answer 5

so then \[R(x) = -0.02x^4-0.3x^3 + 4.4x^2 -14.2x\] ???

Answer 6

@phi did I get it right?

Answer 7

to multiply out
(0.2x + 5)(-0.1x³ + x² - 3x + 4)
you would do
0.2x(-0.1x³ + x² - 3x + 4) + 5(-0.1x³ + x² - 3x + 4)
distribute the .2x on the first term, and 5 on the 2nd
combine "like terms"
what do you get for the first part: 0.2x(-0.1x³ + x² - 3x + 4)

Answer 8

\[-0.02x^4 + 0.2x^3 - 0.6x^2 + 0.8x + 0\]

Answer 9

yes, now the 2nd term, distribute the 5
5(-0.1x³ + x² - 3x + 4)

Answer 10

it looks like your original answer is correct except it is missing the last term.

Answer 11

And then the second is

\[-0.5x^3 +5x^2 - 15x + 20 \]

Answer 12

yes, now combine them. You get what you had, except for a 20 you left off, the first time.

Answer 13

So what I get is:

\[0.01x^7 - 0.2x^6 + 1.6x^5 - 6.8x^4 + 17x^3 - 24x^2 + 16x \]

Answer 14

I multiply them together right?

Answer 15

no, you add them

Answer 16

.... Okay, my mistake! Hold on one sec

Answer 17

you already multiplied them, now you are simplifying

Answer 18

That makes more sense

So now I get\[R(x)=−0.02x^4−0.3x^3+4.4x^2−14.2x + 20\]

Answer 19

yes, looks good

Answer 20

AWESOME!!!!! Thank you so much!

Answer 21

yw