To solve this problem, we take the two points (-3, 3/8) and (2, 12) and substitute them into the generic formula for an exponential function, y = ab^x, where 'a' and 'b' are constants, 'x' is the variable and 'y' is the depended value. This will give us a system of equations that we can solve.
Step 1: Plug the values of the first point into the equation
Let x = -3 and y = 3/8, the equation becomes:
3/8 = a * b^(-3) ----[Equation 1]
Step 2: Plug the values of the second point into the equation
Let x = 2 and y = 12, the equation becomes:
12 = a * b^2 ----[Equation 2]
Now we have a system of two equations, Equation 1 and Equation 2.
We can solve this system simultaneously to find the values of 'a' and 'b'.
Step 3: Solve for 'a' in Equation 1
a = (3/8) * b^3
Step 4: Substitute Equation 3 into Equation 2 to solve for 'b'
12 = ((3/8) * b^3) * b^2.
Simplifying this gives us:
12 = 3b^5/8
Multiply both sides by 8/3 to isolate b^5:
b^5 = 32
The 5th root of both sides gives us:
b = (32)^(1/5)
So, b = 2.
Step 5: Substitute 'b' into Equation 3 to solve for 'a'
Using b = 2 in Equation 3, we get:
a = (3/8) * (2)^3
a = 3/2
So, the formula that passes through the points (-3, 3/8) and (2, 12) is y = (3/2) * 2^x.