Question

On graph points are (-2.75),(-1.5) (0,3),(1,6),(2,12),
Which option is correct exponential equation for the graph
y =2(3)^x, -2(3)^x, 3(2)^x or 3(6)^x

Answer 1

To determine the correct exponential equation for the given points \((-2, 3)\), \((-1, 5)\), \((0, 3)\), \((1, 6)\), and \((2, 12)\), we can substitute these points into each of the given options and see which one fits.

Let's analyze the options one by one, focusing particularly on the points provided:

1. **Option A: \(y = 2(3)^x\)**
- \(x = 0\): \(y = 2(3^0) = 2\) (Mismatch)
- (Does not match the point (0, 3))

2. **Option B: \(y = -2(3)^x\)**
- \(x = 0\): \(y = -2(3^0) = -2\) (Mismatch)
- (Does not match the point (0, 3))

3. **Option C: \(y = 3(2)^x\)**
- \(x = 0\): \(y = 3(2^0) = 3\) (Match)
- \(x = 1\): \(y = 3(2^1) = 6\) (Match)
- \(x = 2\): \(y = 3(2^2) = 12\) (Match)
- \(x = -1\): \(y = 3(2^{-1}) = 1.5\) (Not part of the original points)
- \(x = -2\): \(y = 3(2^{-2}) = 0.75\) (Not part of the original points)

4. **Option D: \(y = 3(6)^x\)**
- \(x = 0\): \(y = 3(6^0) = 3\) (Match)
- \(x = 1\): \(y = 3(6^1) = 18\) (Mismatch)
- (Does not match the point (1, 6))

From the checks, it appears that **Option C: \(y = 3(2)^x\)** fits most of the provided points, specifically (0, 3), (1, 6), and (2, 12).

**Conclusion: The best fit is \(y = 3(2)^x\).**