Question

PLEASE HELPP
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
A
The exponential function decays at one-half the rate of the quadratic function.
B The exponential function decays at the same rate as the quadratic function.
C The exponential function decays at two-thirds the rate of the quadratic function.
D The exponential function decays at three-fourths the rate of the quadratic function.

Answer 1

The Decay rate for any  function can be calculated by the formula Decay rate = [ difference in y values ÷difference in x values in given interval.].

Decay Rate for the exponential function in the interval -2≤x≤0. is (4-1)÷(-2-0)

= 3÷2.

Decay rate for quadratic function in same interval =[ (4-0)÷-(-2-0)] = 2÷1.

Ratio of decay rates=$\frac{3}{2} :\frac{2}{1}=3:4.$

Option D The exponential function decays at three-fourths the rate of the quadratic function. is the right answer.

Answer 2

Answer:

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

Step-by-step explanation:

We calculate the average slope of each graph in the indicated interval, the slope can be calculated as m=(y2-y1)/(x2-x1)

For the exponential function

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

For the quadratic function

$m_q=\frac{4-0}{-2-0}=-\frac{4}{2}  =-2$

If we calculated de ratio of both average slopes:

$\frac{m_e}{m_q}=\frac{-\frac{3}{2} }{-2}  = \frac{3}{4}$

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