Respuesta :
Answer:
9 years.
Step-by-step explanation:
For 50 raccoons the equation is
0.4x^2+2x+2 = 50
0.4x^2+2x - 48 = 0
x = [-2 +/- sqrt(2^2- 4* 0.4*(-48)] / (2*0.4)
= (-2 +/- sqrt 9) / 0.8
= 8.74 , - 13.75 (ignore the negative).
So it's 9 years.
A function assigns the values. The time when there were 50 racoons in the area is 8.736 years.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Given that the number y of raccoons in an area after x years can be modelled by the function y= 0.4x²+2x+2. Therefore, there were 50 racoons in the area at time,
50 = 0.4x² + 2x + 2
0.4x² + 2x - 48 = 0
[tex]x = \dfrac{-2 \pm \sqrt{2^2 - 4(0.4)(-48)}}{2(0.4)}\\\\x = \dfrac{-2 \pm \sqrt{4 + 76.8}}{0.8}\\\\x = \dfrac{-2 \pm 8.9888}{0.8}\\\\x = 8.736, -13.736[/tex]
Since the time can not be negative, Hence, the time when there were 50 racoons in the area is 8.736 years.
Learn more about Function:
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