Chapter 2.2, Problem 6E

Solution

Determine whether the function $KE\left(v\right)=\frac{1}{2}k{v}^2$ is a power function, given that $c,g,k,\text{and}\pi$ represents constants. If it is a power function, state the power and constant of variation.

It is a power function.

Constant of variation is $\frac{1}{2}k$ .

And the power is $2$ .

Given:

  $KE\left(v\right)=\frac{1}{2}k{v}^2$ .

Concept Used:

• A power function can be represented in the form $P\left(x\right)=k\cdot x^a$, here k is the constant of variation and a is the power.

Calculation:

The given function is $KE\left(v\right)=\frac{1}{2}k{v}^2$ .

It is in the form of $P\left(x\right)=k\cdot x^a$ .

Hence, it is a power function.

Constant of variation is $\frac{1}{2}k$ .

And the power is $2$ .