Question

A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the interval -2

Answer 1

To check the decay rate, we need to check the variation in y-axis.

Since our interval is

$-2We need to evaluate both function at those limits.

At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).

[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}$

To compare the decay rates we need to check the variation on the y-axis of both functions.

$\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}$

Now, we calculate their ratio to find how they compare:

$\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}$

This tell us that the exponential function decays at three-fourths the rate of the quadratic function.

And this is the fourth option.