A math problem, for you self professed math enthusiasts

[Akaiyou]

So i have the following math problem and im stumped.

A department store's revenue, in millions, can be approximated using the equation R=-0.57y^2+28.88y+115.01, where R represents the revenue each year from 1998 to 2004 and y represents the number of years since 1998, which corresponds to y=0. In what year between 1998 and 2004 did the department store's revenue reach $249 million?

Anyone know the answer? An explanation on how to solve this would also be great.

[DarkLink]

So we want to know y for R=249. That makes the equation look like this:

249=-.57y^2+28.88y+115.01

From here, you can use the quadratic formula to find possible solutions for y, we just have to slightly re-arrange things. We want the ax^2+bx+c to equal 0, so we subtract 249 from both sides of the equation to get this:

0=-.57y^2+28.88y-133.99

So:
a=-.57
b=28.88
c=-133.99

We then use the quadratic equation:

y=(-b+SQRT(b^2-4ac))/(2a)

and/or

y=(-b-SQRT(b^2-4ac))/(2a)

Plug in a, b, and c to get the two possible answers. Take those two numbers and plug them back into the original equation, and you should get a correct answer.

Incidentally, the two roots we get are 5.166, and 45.500. So revenue will be equal to 249 at years 5.166 and 45.5. If you graph the equation, you can see that 5.2 years is the value we're looking for in the problem, as year 45.5 is well past 2004.

Answer: y=2003.2

[Wolfshade]

Good ol' quadratic formula!

[Psychosplodge]

Do your own maths homework

[lobster-overlord]

Read the company's annual profit reports and skip all the math. Much quicker ;-)

( I'm also the guy who solves the rubick's cube by taking it apart and rebuilding it from scratch--our version was molded plastic colors, not stickers, so I didn't learn it the 'rearrange stickers' way.)

Sorry for that tangent on this. Wow, this thread really brings back not only memories of 5 years of Honors/AP math classes, but also the uneasy feelings I got when I dumped them infavor of social sciences in college :-)

[DarkLink]

It's a lot easier than matrices, linear analysis, and finite element analysis.

[Wolfshade]

It's simple quadratics this is secondary school stuff.