Question

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The x axis ranges from 0 to 3.2 in increments of 0.2 and the y axis ranges from 0 to 20 in increments of 2. The curve labeled f of x equals 1.8 to the power of x passes through left parenthesis 0 comma 1 right
parenthesis, left parenthesis 1 comma 1.8 right parenthesis, left parenthesis 2 comma 3.24 right parenthesis, approximately left parenthesis 2.7 comma 4.8 right parenthesis, and left parenthesis 3 comma 5.832
right parenthesis. The line labeled g of x equals 1.8 times x passes through left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 1.8 right parenthesis, left parenthesis 2 comma 3.6 right
parenthesis, approximately left parenthesis 2.7 comma 4.8 right parenthesis, and left parenthesis 3 comma 5.4 right parenthesis.

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Austin is using graphs to compare the growth rates of g (x) = 1.3x and f(x) =1.3. Which statement is true?

(1 point)

The growth rate of f (z) = 1.8 is greater than the growth rate of g (x) = 1.8x when x is greater than approximately 2.2.

O The growth rate of f (x) = 1.87 is less than the growth rate of g (x) = 1.8x until x is approximately 2.7.

The growth rate of f (x) = 1.87 is greater than the growth rate of g (x) = 1.8x when x is less than 1.

O The growth rate of g (x) = 1.8x is only greater than the growth rate of f () = 1.8 when x is between 1 and approximately 2.7.

Answer 1

Answer: The second statement (The growth of f(x)=1.8^x is less than the growth of g(x)=1.8x until x ≈ 2.7).

Reason: f(2)=3.24 < g(2)=3.6 and f(3)=5.832 > g(3)=5.4, so the exponential is below the line until it crosses between 2 and 3 (about x ≈ 2.7), after which f(x) grows faster.