Which of the following exponential functions goes through the points (1, 6) and (2, 12)?
A.f(x)= 3(2)^x
B.f(x)= 2(3)^x
C.f(x)= 3(2)^-x
D.f(x)= 2(3)^-x
A does
Thank You
To determine which exponential function goes through the points (1, 6) and (2, 12), we can substitute the values into each function and see which one satisfies both equations.
Let's start with option A:
A. f(x) = 3(2)^x
For (1, 6):
f(1) = 3(2)^1 = 3(2) = 6 ✔️
For (2, 12):
f(2) = 3(2)^2 = 3(4) = 12 ✔️
Option A satisfies both equations.
Now let's check option B:
B. f(x) = 2(3)^x
For (1, 6):
f(1) = 2(3)^1 = 2(3) = 6 ✔️
For (2, 12):
f(2) = 2(3)^2 = 2(9) = 18 ❌
Option B does not satisfy the second equation.
Now let's check option C:
C. f(x) = 3(2)^-x
For (1, 6):
f(1) = 3(2)^-1 = 3(1/2) = 1.5 ❌
Option C does not satisfy the first equation.
Lastly, let's check option D:
D. f(x) = 2(3)^-x
For (1, 6):
f(1) = 2(3)^-1 = 2(1/3) = 2/3 ❌
Option D does not satisfy the first equation.
Therefore, the exponential function that goes through the points (1, 6) and (2, 12) is option A, f(x) = 3(2)^x.
To determine which exponential function goes through the given points (1, 6) and (2, 12), we can substitute the x and y values into each of the options and check which function satisfies both points.
Let's substitute the points (1, 6) into each option:
A. f(x) = 3(2)^x
Substituting x = 1: f(1) = 3(2)^1 = 6 (satisfies the point (1, 6))
Substituting x = 2: f(2) = 3(2)^2 = 12 (satisfies the point (2, 12))
B. f(x) = 2(3)^x
Substituting x = 1: f(1) = 2(3)^1 = 6 (satisfies the point (1, 6))
Substituting x = 2: f(2) = 2(3)^2 = 18 (does not satisfy the point (2, 12))
C. f(x) = 3(2)^-x
Substituting x = 1: f(1) = 3(2)^-1 = 1.5 (does not satisfy the point (1, 6))
D. f(x) = 2(3)^-x
Substituting x = 1: f(1) = 2(3)^-1 = 2/3 (does not satisfy the point (1, 6))
Thus, the only option that goes through both points (1, 6) and (2, 12) is option A, f(x) = 3(2)^x.