Ranking Average Values of Functions

Question

The table below gives four functions and their corresponding average values on the interval $$[0,2]$$. Which of the following lists the functions in increasing order of their average value?

| Function          | Interval  | Average Value (Exact or Approx.)          |
|-------------------|-----------|-------------------------------------------|
| $$f(x)=e^{-2x}$$  | $$[0,2]$$ | $$\frac{1-e^{-4}}{4}\approx0.2454$$       |
| $$f(x)=e^{-x}$$   | $$[0,2]$$ | $$\frac{1-e^{-2}}{2}\approx0.4323$$       |
| $$f(x)=e^{-0.5x}$$| $$[0,2]$$ | $$\frac{1-e^{-1}}{1}\approx0.6321$$       |
| $$f(x)=1$$        | $$[0,2]$$ | $$1$$                                     |

Accepted Answer

$$e^{-2x}$$, $$e^{-x}$$, $$e^{-0.5x}$$, $$1$$

Answer

$$e^{-x}$$, $$e^{-2x}$$, $$e^{-0.5x}$$, $$1$$

Answer

$$1$$, $$e^{-0.5x}$$, $$e^{-x}$$, $$e^{-2x}$$

Answer

$$e^{-2x}$$, $$e^{-0.5x}$$, $$e^{-x}$$, $$1$$

Function	Interval	Average Value (Exact or Approx.)
$f(x)=e^{-2x}$	$[0,2]$	$\frac{1-e^{-4}}{4}\approx0.2454$
$f(x)=e^{-x}$	$[0,2]$	$\frac{1-e^{-2}}{2}\approx0.4323$
$f(x)=e^{-0.5x}$	$[0,2]$	$\frac{1-e^{-1}}{1}\approx0.6321$
$f(x)=1$	$[0,2]$	$1$

Ranking Average Values of Functions

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