Instructions: Graph the following function. Then, state whether the function represents exponential growth or decay.y=(45)x𝑦=(45)𝑥This function is exponential
Question
Instructions:
Graph the following function. Then, state whether the function represents exponential growth or decay.
Function:
This function is exponential.
Solution
To graph the function y = 45^x, you would follow these steps:
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Identify the base, which is 45. This is a constant that is raised to the power of x.
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Create a table of values to plot on the graph. Choose a few values for x (both positive and negative) and calculate the corresponding y values. For example, if x = -1, y = 1/45. If x = 0, y = 1. If x = 1, y = 45. If x = 2, y = 2025, and so on.
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Plot these points on a graph. The x-values will be along the horizontal axis and the y-values along the vertical axis.
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Draw a smooth curve through the points. The curve should start from the y-axis (if extended to negative infinity for x) and rise to the right.
This function represents exponential growth because the base of the exponent (45) is greater than 1. This means as x increases, y will also increase at an increasing rate.
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