Question
Graph the exponential function.
y = 2(4.5)^x
y = 2(4.5)^x
Answers
Answered by
GPT 3.5
To graph the exponential function y = 2(4.5)^x, we will plot several points and then connect them to create a smooth curve.
For this function, we can choose any values for x and then calculate the corresponding y-values.
Let's choose x = -2, -1, 0, 1, and 2:
When x = -2, y = 2(4.5)^(-2) = 2(1/20.25) = 2/20.25 ≈ 0.0988
When x = -1, y = 2(4.5)^(-1) = 2(1/4.5) ≈ 0.44
When x = 0, y = 2(4.5)^0 = 2(1) = 2
When x = 1, y = 2(4.5)^1 = 2(4.5) = 9
When x = 2, y = 2(4.5)^2 = 2(20.25) = 40.5
Now, let's plot these points on a graph:
(-2, 0.0988), (-1, 0.44), (0, 2), (1, 9), (2, 40.5)
Note: Since exponential functions grow rapidly, it is recommended to choose additional points both before and after the chosen x-values to better understand the shape of the curve.
To connect these points and draw the graph, we get a smooth curve that increases rapidly as x moves to the right. The y-values increase exponentially as x increases.
Here is the graph of y = 2(4.5)^x:
(see attachment)
For this function, we can choose any values for x and then calculate the corresponding y-values.
Let's choose x = -2, -1, 0, 1, and 2:
When x = -2, y = 2(4.5)^(-2) = 2(1/20.25) = 2/20.25 ≈ 0.0988
When x = -1, y = 2(4.5)^(-1) = 2(1/4.5) ≈ 0.44
When x = 0, y = 2(4.5)^0 = 2(1) = 2
When x = 1, y = 2(4.5)^1 = 2(4.5) = 9
When x = 2, y = 2(4.5)^2 = 2(20.25) = 40.5
Now, let's plot these points on a graph:
(-2, 0.0988), (-1, 0.44), (0, 2), (1, 9), (2, 40.5)
Note: Since exponential functions grow rapidly, it is recommended to choose additional points both before and after the chosen x-values to better understand the shape of the curve.
To connect these points and draw the graph, we get a smooth curve that increases rapidly as x moves to the right. The y-values increase exponentially as x increases.
Here is the graph of y = 2(4.5)^x:
(see attachment)