which statement is true?\nthe growth rate of the exponential function exceeds the growth rate of the linear…

which statement is true?\nthe growth rate of the exponential function exceeds the growth rate of the linear function for -1≤x≤3.\nthe growth rate of the exponential function exceeds the growth rate of the linear function for 0≤x≤3.\nthe growth rate of the exponential function exceeds the growth rate of the linear function for -1≤x≤1.\nthe growth rate of the exponential function exceeds the growth rate of the linear function for 1≤x≤3.
Answer
Explanation:
Step1: Analyze the graph
Observe the graph of the exponential and linear - function. The growth rate of a function is related to its steepness.
Step2: Identify the intersection point
The two functions intersect at the point $(1,7)$. Before the intersection point, the linear function is steeper (has a greater growth rate in some intervals), and after the intersection point, the exponential function becomes steeper.
Step3: Determine the interval
For $x$ values from $1$ to $3$, the exponential function is steeper than the linear function, which means the growth rate of the exponential function exceeds the growth rate of the linear function in the interval $1\leq x\leq3$.
Answer:
The growth rate of the exponential function exceeds the growth rate of the linear function for $1\leq x\leq3$.