Q4. - Algebra 2

Question

Match each function with its graph.

$y=2{\left(5\right)}^x$

Step-by-Step Solution

Answer

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

Step 1. Given Information.

The function $y=2{\left(5\right)}^x$ 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 $x=0$:

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

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