# Question Video: Forming the Equation of an Exponential Function from Its Graph Mathematics • 9th Grade

Observe the given graph, and then answer the following questions. Find the π¦-intercept in the shown graph. As this graph represents an exponential function, every π¦-value is multiplied by π when π₯ increases by Ξπ₯. Find π for Ξπ₯ = 1. Find the equation that describes the graph in the form π¦ = ππ^(π₯/Ξπ₯).

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### Video Transcript

Observe the given graph and then answer the following questions. Find the π¦-intercept in the shown graph. As this graph represents an exponential function, every π¦-value is multiplied by π when π₯ increases by Ξπ₯. Find π for Ξπ₯ equals one. Find the equation that describes the graph in the form π¦ equals ππ to the power of π₯ over Ξπ₯.

Letβs begin by finding the graphβs π¦-intercept. We can see that the line of the graph passes through the point zero, 10. Therefore, the π¦-intercept is 10. Now, letβs find the value of π in the equation of the graph. In the problem, we are told that the graph represents an exponential function for which every π¦-value is multiplied by π when π₯ increases by Ξπ₯. And weβre asked to find π when Ξπ₯ equals one. Weβve already seen that the graph passes through the point zero, 10. And we can also see that it passes through the point one, 20. The change in π₯ between these two points is one, so it satisfies Ξπ₯ equals one.

We are told that the π¦-value is multiplied by π when π₯ increases by Ξπ₯. If the π¦-value of our first point is π¦ one and the π¦-value of our second point is π¦ two, then π equals π¦ two over π¦ one which is equal to 20 divided by 10, which is equal to two. And finally, we need to find the equation that describes the graph in the form π¦ equals ππ to the power of π₯ over Ξπ₯. We are already given Ξπ₯ equals one, and we have found the value of π equal to two. Therefore, π¦ equals π times two to the π₯ over one, which is just equal to π times two to the π₯. To find the value of π, we can substitute the π₯- and π¦-values of points we know to be on the graph.

Weβve already found the π¦-intercept to be 10, so we know that the point zero, 10 lies on the graph. This means we can substitute the values of π₯ equals zero and π¦ equals 10 into the equation which gives us 10 equals π times two to the zero. By the zero-exponent rule, two to the zero is just equal to one. Therefore, this gives π equals 10. This gives us our equation and the final answer π¦ equals 10 times two to the π₯.