The net income y (in millions of dollars) of Pet Products Unlimited from 1997 to 1999 is given by the equation

Question

y = 9x(squared) + 15x + 52, where x represents the number of years after 1997. Assume this trend continues and predict the year in which Pet Product Unlimited's net income will be $598 million."

Please inform me not only the answer, but more imprortantly how you came to your solution. Thanks

Answer 1

9x^2 + 15x + 52 = 598 as given

9x^2 + 15x - 546 = 0

Dividing by 3, we get

3x^2 + 5x - 182 = 0

This is a quadratic equation of the form ax^2 + bx + c = 0 and here we have

a = 3, b = 5 and c = - 182

The roots x1 and x2 of the quadratic equation are

x1 = [-b + sqrt(b^2 - 4ac)] / 2a and

x2 = [-b - sqrt(b^2 - 4ac)] / 2a respectively.

So, we have

x1 = [-5 + sqrt(25 - 4x3x-182)] / 6

= [-5 +sqrt(25 + 2184)] / 6

= [ -5 + sqrt (2209) ] / 6

We need not compute x2 since the value will be negative and has no real significance.

x1 = [ - 5 + 47 ] / 6

= 42 / 6

= 7

So, the income will become $598 in the year 2004 (1997 + 7)

Answer 2

Method one, trail and error.
Start off with year one, and put this value into the equation.
Then year two, then year three and so on until you get the answer (assuming it's an exact year).

For first year.
y = 9x² + 15x + 52.
y = 9(1)² + 15(1) + 52
y = 9 + 15 + 52
y = 76m.

For second year.
y = 9x² + 15x + 52.
y = 9(2)² + 15(2) + 52
y = 36 + 30 + 52
y = 118m.

↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

For 7th year.
y = 9x² + 15x + 52.
y = 9(7)² + 15(7) + 52
y = 441 + 105 + 52
y = 598m.


Another method.
y = 9x² + 15x + 52
598 = 9x² + 15x + 52
0 = 9x² + 15x + 52 - 598
0 = 9x² + 15x - 546
Solve the quadratic equation with: [-b ± √(b² - 4ac)] / 2a
x = 7 or x = -8∙666...
Taking positive value, x = 7, that is Seven years.

Answer 3

sol is 7