Final answer:
By substituting the given points into the exponential function equation and solving for a and b, we find that the correct function is y = 2×3^x, which is option a.
Step-by-step explanation:
We need to determine which of the given exponential functions passes through the points (0, 2) and (4, 162) by substituting these values into the general form y = abx and solving for a and b.
First, let's use the point (0, 2). Plugging in x = 0 and y = 2:
2 = a * b0 => 2 = a * 1 => a = 2
Now we know that a must be 2 because b0 is always 1, regardless of the value of b. Next, let's use the point (4, 162) and the already determined value of a:
162 = 2 * b4 => 81 = b4
To find b, we take the fourth root of both sides:
b = 811/4 => b = 3
Therefore, the correct exponential function is y = 2 * 3x, which is option a.