Given the following graph of f, which is the best approximation for ?

Question

Given the following graph of f, which is the best approximation for  ?

Quizplus · Accepted Answer

The graph shows that f increases steadily from $50,000 to $100,000 as x increases from 0 to 5.5. To estimate f(5.6), we can assume the same rate of increase and find the corresponding increase from x = 5.5 to x = 5.6. The distance between 5.5 and 5.6 is 0.1, which is 1/55 of the entire x interval from 0 to 5.5 (which is 5.5). Therefore, we can estimate the increase in f by dividing the total increase from $50,000 to $100,000 by 55 and multiplying by 1:

increase ≈ ($100,000 - $50,000)/55 ≈ $909.09

Starting from f(5.5) ≈ $78,750, we can add the estimated increase to obtain:

f(5.6) ≈ $78,750 + $909.09 ≈ $79,659.09

The closest choice to this estimate is B) $78,750.

Given the Following Graph of F, Which Is the Best