Chapter 7.6, Problem 16PPE

To determine

Toevaluate:The function for the given value.

Answer to Problem 16PPE

The value of function $y\left(x\right)=20\cdot {0.5}^x$ for $x=3$ is 2.5.

Explanation of Solution

Given information:

The given function $y\left(x\right)=20\cdot {0.5}^x$ is to be evaluate for $x=3$ .

Methodused:

Function is calculated by substituting the value of domain point (variable).

Calculations:

The given function is $y\left(x\right)=20\cdot {0.5}^x$ , and the required value is $y\left(3\right)$ .

  $y\left(x\right)=20\cdot {\left(0.5\right)}^x$

  $\Rightarrow y\left(3\right)=20\cdot {\left(\frac{5}{10}\right)}^3$

  $\Rightarrow y\left(3\right)=20\cdot {\left(\frac{1}{2}\right)}^3$

  $\Rightarrow y\left(3\right)=20\cdot \frac{1}{8}$

  $\Rightarrow y\left(3\right)=\frac{5}{2}=2.5$

Thus, the value of function $y\left(x\right)=20\cdot {0.5}^x$ for $x=3$ is 2.5.

Conclusion:

The value of function $y\left(x\right)=20\cdot {0.5}^x$ for $x=3$ is 2.5.