Chapter 6.1, Problem 45E

a.

To determine

To graph: the function and describe the domain and range.

Answer to Problem 45E

Domain :{ 0, 1, 2, 3…}

Range: {1, 0.25, 0.025, ….}

Explanation of Solution

Given information: The function $y={0.25}^x$ represents the percentage of the original

screen display that see, where x is the number of times zoom in.

Calculation:

Graph $y={0.25}^x$ which passes through (0, 1) and (1, 0.25) is shown below.

  

From the graph, the domain is all real numbers and the range is y > 0. However, the context of the situation tells us that x must be a nonnegative integer so the domain is the set of all natural numbers: {0, 1, 2, 3...}. This will give us a range of powers of 0.25 starting from ${0.25}^0=1$ :{ 1, 0.25, 0.0625 ...}

b.

To determine

To find: and interpret the y -intercept.

Answer to Problem 45E

The y -intercept is (0, 1) $\to$ b = 1 which is the value of the function when x = 0.

Explanation of Solution

Given information:

Calculation:

The y -intercept is (0, 1) $\to$ b = 1 which is the value of the function when x = 0.

c.

To determine

To zoom: twice find what percentage of the original screen does see.

Answer to Problem 45E

The screen now is 6.25% of the size of the original screen.

Explanation of Solution

Given information: $y={0.25}^x$

Calculation:

  $\begin{array}{c}y={0.25}^x\\ x=2\\ y={0.25}^2=0.0625\end{array}$

The screen now is 6.25% of the size of the original screen.