# Computer Sales

1. Sep 25, 2016

### Veronica_Oles

1. The problem statement, all variables and given/known data
Between 1985 and 1995 the number of computers in thousands sold in canada is estimated by c(t) = 0.92(t^3 + 8t^2 + 40t +400)
In what year did home computers sale reach 1.5 million?
2. Relevant equations

3. The attempt at a solution
I know I have to isolate the t to obtain time. So far this is what I have gotten up to

1230.43 = t^3 + 8^2 + 40t
Here is where I am stuck. Would I have to factor out a t in order to move on to th next step?

2. Sep 25, 2016

### Math_QED

There are formulas to find the roots of any third degree polynomial. However, I assume that you did not cover those formulas in class. In exercises where you are not allowed to use a calculator, you can 'guess' one of the roots and then use something like synthetic division to find the remaining quadratic polynomial. In this case however, this seems quite impossible so I would use a calculator. Note too that you wrote 8^2 instead of 8t^2.

3. Sep 25, 2016

### Staff: Mentor

The second term on the right should be 8t2. I'm assuming, but didn't verify, that the 1230.43 number has the 400 term already folded in.

Although there is a technique for solving third-degree polynomials, it's not something I have committed to memory, and it's very complicated. One approach would be to graph the equation C = t3 + 8t2 + 40t, and find the point at which the C value is at or close to 1230.43, then read off the t value at that point.

Another approach is to start with an education guess, say t = 10, and see what C value you get, adjusting t up or down in successive calculations.

4. Sep 25, 2016

### SammyS

Staff Emeritus
Factoring is only useful for the case where the othe side of the equation is zero.

By the way, what is the definition of the variable, t ?

5. Sep 25, 2016

### Veronica_Oles

Sorry about that I meant 8t^2. The book uses a graphing calculator however we were meant to solve it algebraically:/

6. Sep 25, 2016

### Veronica_Oles

T is for time.

7. Sep 25, 2016

### Ray Vickson

The exact solution is very complicated to get. Typically in such a problem, we unashamedly employ numerical methods, such as graphical analysis, resorting to a spreadsheet or computer algebra system, or using a decent scientific calculator.

For an exact method, see, eg.,
http://www.math.vanderbilt.edu/~schectex/courses/cubic/

Last edited: Sep 25, 2016
8. Sep 25, 2016

### SammyS

Staff Emeritus
Yes, time. But how is that time measured?
For the year 1985 is t = 1985 ?