I have been trying this on my own and just want to know if this is right are not
2. Suppose that the linear equation y = 0.3x + 0.9 represents an estimate of the average cost of gas for year x starting in 2002. The year 2002 would be represented by x = 1, for example, as it is the first year in the study. Similarly, 2008 would be year 7, or x = 7.
a) What year would be represented by x = 2? (2 pts.) 2003
b) How much did it cost per gallon of gasoline in the year represented by x=2? (2 pts.)
so does the y represent 2003= 0.3x + 0.9
0.3x 0.9 =2003
0.3x=2002.1
0.3x/0.3=2002.1/0.3
x=2002.1/0.3
x=667367
I do not think this is right
c) What x-value represents the year 2011? (2 pts.)10
d) Assuming this growth trend continues, what will the price of gasoline be in the year 2011? How did you arrive at your answer? Show your work (2 pts.)this i am not sure about at all do I need to subtract this one
costofgasaoline in 2003=.3(2)+.9=1.5
costofgasoline in 2011=.3(10)+.9=3.9
check that.
thank you so do you think the way I did is also right
I think you should not have inputted the year. X=YEAR-2001
so for 2003, X=2003-2001=2
and for 2010, X=2011-2001=10
To find the answers to parts (a) and (c) correctly, you need to substitute the given values of x into the equation y = 0.3x + 0.9. Let's go through the steps.
a) To find the year represented by x = 2, substitute x = 2 into the equation.
y = 0.3x + 0.9
y = 0.3(2) + 0.9
y = 0.6 + 0.9
y = 1.5
Therefore, the year represented by x = 2 is 1.5 or 2003.
b) Now, to find the cost per gallon of gasoline in the year represented by x = 2, you need to substitute the value of y = 1.5 back into the equation.
y = 0.3x + 0.9
1.5 = 0.3x + 0.9
0.3x = 1.5 - 0.9
0.3x = 0.6
x = 0.6 / 0.3
x = 2
So, the cost per gallon of gasoline in the year represented by x = 2 is twice the value of x. This means that the cost is 2 times 0.3 plus 0.9, which equals 1.5.
c) To find the x-value representing the year 2011, set y equal to 2011 and rearrange the equation.
0.3x + 0.9 = 2011
0.3x = 2011 - 0.9
0.3x = 2010.1
x = 2010.1 / 0.3
x ≈ 6703.33
Therefore, the x-value representing the year 2011 is approximately 6703.33 or simply 10 (rounded to the nearest whole number).
d) Based on the linear equation provided, it is not appropriate to assume that the growth trend will continue indefinitely. Therefore, we cannot accurately predict the price of gasoline in the year 2011 using this equation.