Question

A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval


The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.

Answer 1

The exponential function decays at three-fourths the rate of the quadratic function.

The given inequality is -2≤x≤0.

We need to determine how do the decay rates of the functions compare over the interval.

What is the quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

We calculate the average slope of each graph in the indicated interval, the slope can be calculated as $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$.

Now, for the exponential function:

$m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}$

For the quadratic function:

$m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2$

Now, the ratio of both average slopes is$\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}$.

Therefore, the exponential function decays at three-fourths the rate of the quadratic function.

To learn more about the exponential function visit:

https://brainly.com/question/11487261.

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