To graph the function \( y = 15(2^x) \) and find the y-intercept, we need to evaluate the function when \( x = 0 \).
- Finding the y-intercept: \[ y = 15(2^0) \] Since \( 2^0 = 1 \), \[ y = 15 \times 1 = 15 \]
So, the y-intercept is \( (0, 15) \).
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Graphing the function: To graph the function \( y = 15(2^x) \), we can calculate a few additional points by selecting values for \( x \):
- For \( x = -1 \): \[ y = 15(2^{-1}) = 15 \times \frac{1}{2} = 7.5 \quad \text{(Point: (-1, 7.5))} \]
- For \( x = 1 \): \[ y = 15(2^1) = 15 \times 2 = 30 \quad \text{(Point: (1, 30))} \]
- For \( x = 2 \): \[ y = 15(2^2) = 15 \times 4 = 60 \quad \text{(Point: (2, 60))} \]
Now, you can plot these points on the graph:
- The point \( (0, 15) \) is the y-intercept.
- The point \( (-1, 7.5) \) is close to the y-axis.
- The points \( (1, 30) \) and \( (2, 60) \) show the rapid increase of the function as \( x \) increases.
The graph will show exponential growth as \( x \) increases. The y-intercept is \( 15 \) at \( (0, 15) \).
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