To determine the correct exponential equation based on the description provided, let's analyze what we know:
- The curve passes through points in quadrants 1 and 2 of the coordinate plane, indicating that the function is positive for those points.
- Since the curve has arrows at both ends, it indicates that the graph will either rise sharply in both directions (for a positive base greater than 1) or drop quickly (for a negative base less than 1). However, since the graph is in the positive quadrants, the base should be greater than 1.
Given the options:
- Option #1: \( y=2(3)^x \) → Positive, base of 3 (greater than 1)
- Option #2: \( y=-2(3)^x \) → Negative, does not fit since it would not pass through quadrants 1 and 2.
- Option #3: \( y=3(2)^x \) → Positive, base of 2 (greater than 1)
- Option #4: \( y=3(6)^x \) → Positive, base of 6 (greater than 1)
Options #1, #3, and #4 are all positive, but we need to choose the one that likely fits the description. The exponential functions grow differently based on their base:
- Option #1 with base 3 would grow more rapidly than Option #3 with base 2.
- Option #4 (base 6) would grow much faster than Options #1 and #3.
If the graph shows a pronounced exponential growth, then it is likely Option #4 \( y=3(6)^x \).
However, without the image to confirm the steepness or position of the curve, we can conclude that based on typical choices, the best candidate for an exponential growth curve passing through points in the first two quadrants is likely Option #4.
Thus, the answer would be:
Option #4 is the correct equation for the graph.
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