Chapter 10: Q4. (page 527)

Match each function with its graph.
$y = 2 {(5)}^{x}$

Short Answer

Expert verified

$y = 2 {(5)}^{x}$ is represented by the graph:

Step by step solution

Step 1. Given Information.

The function $y = 2 {(5)}^{x}$ is to be matched with its graph among the following:

Step 2. Explanation.

A function is said to be exponential is the variable is in the exponent i.e., of the form $y = a b^{x} + c$

The function has x in the exponent i.e., the degree of the function is a variable.

Hence the function is an exponential function.

And since the base is greater than 1, the function is an increasing function.

Hence the graph is either option a or c.

Also, when $x = 0$ :

$\begin{array}{l} y = 2 {(5)}^{x} \\ y = 2 {(5)}^{0} \\ y = 2 (1) \\ y = 2 \end{array}$

Among options a and c, the graph shown in option a passes through $y = 2$ .

Hence the function is represented by the graph in option a.

Step 3. Conclusion.

Hence, $y = 2 {(5)}^{x}$ is represented by the graph in option a:

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Match each function with its graph.
$y = 2 {(5)}^{x}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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Match each function with its graph.
$y = 2 {(5)}^{x}$