Question

unit 2 linear & exponential functions lesson 11 linear & exponential functions unit test click for long desc consider the graph of function #1 and function #2. how do the growth rates of the two functions compare? (2 points) initially, function #\square has the greater growth rate. by $x = 100$, the growth rate of function #\square surpasses the growth rate of function #\square.

Explanation:

Step1: Analyze Initial Growth Rates

Function #2 is linear (dashed line), Function #1 is exponential (curved line). Initially, the linear function (Function #2) has a steeper slope (greater growth rate) as the exponential starts flat.

Step2: Analyze Growth at \( x = 100 \)

Exponential functions (Function #1) have increasing growth rates (curvature increases), while linear (Function #2) has constant growth. By \( x = 100 \), the exponential (Function #1) has a steeper slope than the linear (Function #2), so its growth rate surpasses.

Answer:

Initially, Function #2 has the greater growth rate. By \( x = 100 \), the growth rate of Function #1 surpasses the growth rate of Function #2.
So the blanks are: 2; 1; 2.