Answer:
D
Step-by-step explanation:
An exponential function which crosses through (1,3) and (2,9) will have a base of 3 since the y values are multiples of 3.
3^1 = 3
3^2 = 9
This means that the function is y = 3^x.
y = 3x
Substitute the two points into the equation y = abx, giving 3 = ab1 and 9 = ab2.
Since a = a, then
3
b1
=
9
b2
, rearranged yields 3b2 = 9b1 → 3b2 − 9b = 0 → b(3b − 9) = 0
Thus, b = 0 or b = 3.
A curve of exponential function never drop below the x-axis, ignore any values of b that are less than or equal to zero.
Therefore, insert b = 3 into
3
b1
= a and
9
b2
= a → a = 1 for both equations.
y = abx
y = (1)(3x)
y = 3x
