Final answer:
By setting the equations of the stock values A(x) and B(x) equal to each other and solving for x, we find that the stocks will have the same value after approximately 12 months, making option d) the correct answer.
Step-by-step explanation:
To find out after how long both stocks will be worth the same amount, we need to set the values of stock A(x) and stock B(x) equal to each other and solve for x.
Step-by-Step Solution:
Equation for stock A: A(x) = 0.65x² - 8x + 10
Equation for stock B: B(x) = 2.35x + 1.25
Set A(x) equal to B(x):
0.65x² - 8x + 10 = 2.35x + 1.25
Bring all terms to one side:
0.65x² - 8x - 2.35x + 10 - 1.25 = 0
Combine like terms:
0.65x² - 10.35x + 8.75 = 0
Now, we must factor or use the quadratic formula to find the value of x. In this case, factoring is complex, so we'll apply the quadratic formula:
x = [-(-10.35) ± √((-10.35)² - 4*0.65*8.75)] / (2*0.65)
Solving this equation gives us two possible values for x, but we are interested in the positive value that represents a realistic number of months:
x ≈ 12.07
Since we can't have a fraction of a month in this context, we round down to the nearest whole month:
x = 12 months
Thus, answer d) 12 months is correct.