After the first round on a television game show, the three contestants have -$300, $600, -$400. Which of the three dollar amount
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Answer:
where f(x) is the bonus every year and x is in number of years
Step-by-step explanation:
The function that represents the situation where $840 annual bonus increases by 5% each year is given by
where f(x) is the bonus every year and x is in number of years
Our function f(x) can be rewritten if we factor out a common x^2 from each term:
Now inside the parentheses we have a polynomial of the form a^2 - b^2, or the difference of two perfect squares, which can be factored as (a+b)(a-b) so we have:
Setting our function equal to zero gives us the roots x = 0, x = 4, and x = -4.
The multiplicity of the root zero is two since it occurs twice, and the others are one since they occur only once. If you graph the function you can see that it will only touch the x-axis at x = 0, but will cross the x-axis at x = 4 and x = -4.
Now inside the parentheses we have a polynomial of the form a^2 - b^2, or the difference of two perfect squares, which can be factored as (a+b)(a-b) so we have:
Setting our function equal to zero gives us the roots x = 0, x = 4, and x = -4.
The multiplicity of the root zero is two since it occurs twice, and the others are one since they occur only once. If you graph the function you can see that it will only touch the x-axis at x = 0, but will cross the x-axis at x = 4 and x = -4.