The projected number N of Wi-Fi enabled cell phones (in millions) in the U.S. can be modeled by the function N=-0.4x^2+21x+35, where x is the number of years since 2009. If the trend continues, find the year in which the projected number of Wi-Fi enabled cell phones will first reach 150 million? Please help!!!! :(
well, just solve
-0.4x^2+21x+35=150
as with most quadratics, it will have two roots. Pick the smallest positive one.
So whats the answer?
To find the year in which the projected number of Wi-Fi enabled cell phones will first reach 150 million, we need to solve the equation N = 150.
The equation for N is given as N = -0.4x^2 + 21x + 35, where x is the number of years since 2009.
Substituting N = 150 into the equation, we have:
150 = -0.4x^2 + 21x + 35
Rearranging the equation to bring all terms to one side:
0.4x^2 - 21x - 35 + 150 = 0
0.4x^2 - 21x + 115 = 0
To solve this quadratic equation for x, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 0.4, b = -21, and c = 115.
Plugging these values into the quadratic formula:
x = (-(-21) ± √((-21)^2 - 4(0.4)(115))) / (2(0.4))
Simplifying:
x = (21 ± √(441 - 184)) / 0.8
x = (21 ± √257) / 0.8
Now we can calculate the values of x:
x₁ = (21 + √257) / 0.8
x₂ = (21 - √257) / 0.8
The positive root x₁ corresponds to the number of years since 2009 when the projected number of Wi-Fi enabled cell phones will first reach 150 million.
x₁ = (21 + √257) / 0.8 ≈ 24.8
Since x represents the number of years since 2009, we add 2009 to get the year:
Year = 2009 + 24.8 ≈ 2033.8
Therefore, the projected number of Wi-Fi enabled cell phones will first reach 150 million around the year 2034.