an exponential function and a linear function are graphed below. over which interval does the growth rate of…

an exponential function and a linear function are graphed below. over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?

an exponential function and a linear function are graphed below. over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?

Answer

Explanation:

Step1: Recall growth - rate concept

The growth rate of a linear function is constant (its slope), and the growth rate of an exponential function $y = a\cdot b^{x}$ is proportional to its value. We can analyze the graph to see where the exponential function is steeper than the linear function.

Step2: Analyze the graph

Looking at the graph, we can see that the exponential function is steeper (has a greater growth - rate) than the linear function for $x>1.79$. Before $x = 1.79$, the linear function may be steeper or they may cross in terms of growth - rate.

Answer:

$x>1.79$