Given that the debt has been represented by the function:
f(x)=-6x^2+8x+50
To get the number of years, x that it would take for the company to be debt free we proceed as follows:
we solve the equation for f(x)=0
hence:
0=-6x^2+8x+50
solving for x using the quadratic formula we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
x=[-8+/-sqrt(8^2-4*(-6)*50)]/(-6*2)
x=[-8+/-√1264]/(-12)
x=27.552
x~28
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Answer:
The number of years after opening its business the company will be out of debt 5.3 years
Step-by-step explanation:
Given
The function f(x)=−4x² + 10x + 60
For the company to be out of debt, then the function must be at least 0
The expression for this is f(x) ≥= 0.
But, we'll be working with the least number of years.
So, we'll make use of f(x) = 0;
Substitution 0 for f(x) in the function
f(x)= −4x² + 10x + 60 becomes
0 = −4x² + 10x + 60 --------- Reorder
4x² - 10x - 60 = 0 ----- Solving this quadratic equation, we have
[tex]x = \frac{-b +- \sqrt{b^{2} - 4ac } }{2a}[/tex]
Where a = 4, b = -10 and c = -60
By Substitution, we have
[tex]x = \frac{- (-10) +- \sqrt{(-10)^{2} - 4 *4 *-60 } }{2 * 4}[/tex]
[tex]x = \frac{10 +- \sqrt{100 + 960 } }{8}[/tex]
[tex]x = \frac{10 +- \sqrt{1060} }{8}[/tex]
[tex]x = \frac{10 +- 32.56 }{8}[/tex]
[tex]x = \frac{10 +32.56 }{8}[/tex] or [tex]x = \frac{10- 32.56 }{8}[/tex]
[tex]x = \frac{42.56 }{8}[/tex] or [tex]x = \frac{-22.56 }{8}[/tex]
[tex]x = 5.32[/tex] or [tex]x = -2.82[/tex]
But number of years can't be negative;
So, [tex]x = 5.32[/tex] years.
[tex]x = 5.3 years[/tex]
Hence, the number of years after opening its business the company will be out of debt 5.3 years
