ANSWER:
1st option: The exponential grows at approximately half the rate of the quadratic
STEP-BY-STEP EXPLANATION:
We compute the rate change in each case, to determine the proportion, just like this:
[tex]f(x)=\frac{f(b)-f(a)}{b-a}[/tex]
We substitute the values in each case:
[tex]\begin{gathered} \text{ Exponential:} \\ \\ f\mleft(x\mright)=\frac{2-1}{1-0}=\frac{1}{1}=1 \\ \\ \text{ Quadratic:} \\ \\ f(x)=\frac{2-0}{1-0}=\frac{2}{1}=2 \\ \\ \text{ Therefore, te ratio would be:} \\ \\ r=\frac{\text{ Exponential}}{\text{Quadratic}}=\frac{1}{2} \\ \\ \end{gathered}[/tex]
Therefore, the correct answer is 1st option: The exponential grows at approximately half the rate of the quadratic
