A) y = 1.5(3)^x
If we plug in x = 0, we get:
y = 1.5(3)^0 = 1.5
However, from the table we can see that when x = 0, y = 2. Therefore, option A is not correct.
B) y = 3(1.5)^x
If we plug in x = 1, we get:
y = 3(1.5)^1 = 4.5
This matches the second value in the table. Let's check the other values:
- When x = 0, y = 3 (matches the first value)
- When x = 2, y = 6.75 (matches the third value)
Therefore, option B is correct.
C) y = 3(0.5)^x
If we plug in x = 0, we get:
y = 3(0.5)^0 = 3
However, from the table we can see that when x = 0, y = 2. Therefore, option C is not correct.
D) y = 0.5(3)^x
If we plug in x = 1, we get:
y = 0.5(3)^1 = 1.5
This does not match the second value in the table. Therefore, option D is not correct.
Therefore, the correct equation that models the exponential data given by the table is:
y = 3(1.5)^x.