Question

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A coordinate plane shows a straight dotted line and an increasing solid curve plotted on it, corresponding to two functions.
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The x-axis shows values from negative 6 to 16 in increments of 2 and the y-axis shows values from negative 10 to 55 in increments of 5. A straight dotted line labeled Function number 1 with a bi-directional arrow passes through left parenthesis 0 comma 1 right parenthesis, left parenthesis 1 comma 5 right parenthesis, left parenthesis 6 comma 25 right parenthesis, left parenthesis 10 comma 41 right parenthesis, and left parenthesis 11.4 comma 46 right parenthesis. A solid curve labeled Function number 2 with a bi-directional arrow passes through left parenthesis negative 6 comma 0 right parenthesis, left parenthesis negative 2 comma 1 right parenthesis, left parenthesis 0 comma 1 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 6 comma 7.5 right parenthesis, left parenthesis 8 comma 15 right parenthesis, left parenthesis 10 comma 30 right parenthesis, and left parenthesis 11.2 comma 46 right parenthesis. The line and the curve intersect at two points: left parenthesis 0 comma 1 right parenthesis and left parenthesis 11.4 comma 46 right parenthesis. All coordinate values are approximate and the coordinates are unlabeled.


Consider the graph of Function #1 which is linear and Function #2 which is exponential. How do the growth rates of the two functions compare?

(2 points)
Initially, Function #
has the greater growth rate. By x=8
, the growth rate of Function #
surpasses the growth rate of Function #
.
Remaining Attempts : 3
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Answer 1

Initially, Function #1 has the greater growth rate. By x = 8, the growth rate of Function #2 surpasses the growth rate of Function #1.

Explanation: Function #1 is linear with constant slope ≈4. Function #2 (exponential) starts with a smaller slope but accelerates; by x≈8 its rate of increase (≈5.6 average between x=6 and x=10) exceeds 4.