Question

The x-axis shows values from negative 70 to 150 in increments of 10 and the y-axis shows values from negative 20,000 to 130,000 in increments of 10,000. A solid curve labeled Function number 1 with a bi-directional arrow passes through left parenthesis negative 70 comma 0 right parenthesis, left parenthesis 0 comma 0 right parenthesis, begins to move upward at left parenthesis 60 comma 0 right parenthesis, passes through left parenthesis 90 comma 5,000 right parenthesis, left parenthesis 100 comma 15,000 right parenthesis, left parenthesis 110 comma 35,000 right parenthesis, left parenthesis 120 comma 90,000 right parenthesis, and left parenthesis 122 comma 122,000 right parenthesis. A dotted straight line labeled Function number 2 with a bi-directional arrow passes through left parenthesis negative 10 comma negative 10,000 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis 100 comma 100,000 right parenthesis, and left parenthesis 130 comma 130,000 right parenthesis. The line and the curve intersect at two points: left parenthesis 0 comma 0 right parenthesis and left parenthesis 122 comma 122,000 right parenthesis. All coordinate values are approximate and the coordinates are unlabeled.Consider the graph of Function #1 and Function #2. How do the growth rates of the two functions compare? (2 points)Initially, Function # has the greater growth rate. By x=100, the growth rate of Function # surpasses the growth rate of Function #.

Answer 1

Initially, Function 2 has the greater growth rate. By x = 100, the growth rate of Function 1 surpasses the growth rate of Function 2.

Explanation: Function 2 is a straight line with constant slope ≈1000 (y increases 100,000 over 100 x‑units), while Function 1 is nearly flat until about x≈60 and then accelerates; after x≈100 its rise is steeper than the line (e.g. y goes from 15,000 at x=100 to 122,000 at x=122).