1)
Since 1960, the number of voters y (in millions) in United States federal elections can be modeled by the function:
y= -0.0006x^3 + 0.0383x^2 + 0.383x + 68.6
where x is the number of years since 1960. According to the model, how many more people voted in 1980 than in 1960? explain the answer.
2)
Can you use the rational zero theorem to find the zeros of the polynomial function:
f(x)= 3x^4 - 2x^3 + 1.5x^2 - 9
Explain why or why not.
Thank you so much!!!!! please help
Since 1960, the number of voters y (in millions) in United States federal elections can be modeled by the function:
y= -0.0006x^3 + 0.0383x^2 + 0.383x + 68.6
where x is the number of years since 1960. According to the model, how many more people voted in 1980 than in 1960? explain the answer.
2)
Can you use the rational zero theorem to find the zeros of the polynomial function:
f(x)= 3x^4 - 2x^3 + 1.5x^2 - 9
Explain why or why not.
Thank you so much!!!!! please help
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1) Substitute x = 0 to find that 68.6 million people voted in 1960.
Then substitute x = 20 (because 1980 = 1960 + 20) to find how many voted in 1980.
The difference is the answer to "how many more".
I leave you to do the calculations.
2) The coefficient 1.5 is a complication, so write the polynomial as
0.5(6x⁴ - 4x³ + 3x² - 18)
Rational zeros of 6x⁴ - 4x³ + 3x² - 18 correspond to factors of the form
(ax + b)
where a is a factor of 6 and b is a factor of 18.
Hence rational zeros can be found by substituting
x = ±1, ±3, ±6, ±9, ±18, ±1/2, ±3/2, ±9/2, ±1/3, ±2, ±1/6 to see if any of these give 0.
[Note 6/2, 18/2, 3/3, 6/3, 9/3, 18/3, 3/6, 6/6, 9/6, 18/6 are repetitions of values already listed.]
Since none of them do give zero, this polynomial has no rational zeros.
Then substitute x = 20 (because 1980 = 1960 + 20) to find how many voted in 1980.
The difference is the answer to "how many more".
I leave you to do the calculations.
2) The coefficient 1.5 is a complication, so write the polynomial as
0.5(6x⁴ - 4x³ + 3x² - 18)
Rational zeros of 6x⁴ - 4x³ + 3x² - 18 correspond to factors of the form
(ax + b)
where a is a factor of 6 and b is a factor of 18.
Hence rational zeros can be found by substituting
x = ±1, ±3, ±6, ±9, ±18, ±1/2, ±3/2, ±9/2, ±1/3, ±2, ±1/6 to see if any of these give 0.
[Note 6/2, 18/2, 3/3, 6/3, 9/3, 18/3, 3/6, 6/6, 9/6, 18/6 are repetitions of values already listed.]
Since none of them do give zero, this polynomial has no rational zeros.
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2) The zeros are 1.4009136... and -1.104899... .
Since the zeros are irrational, I think not.
1) y(1960) = y(0) = 68.6
y(1980) = y(20) = 86.78
18.18 million more voted in 1980 than 1960.
Since the zeros are irrational, I think not.
1) y(1960) = y(0) = 68.6
y(1980) = y(20) = 86.78
18.18 million more voted in 1980 than 1960.