Question

Find the formula for an exponential equation passing through the points (2,3) and (1,4), of the form y = a * bˣ.

a) y = 3 * 2ˣ
b) y = 2 * 3ˣ
c) y = 3 * 3ˣ
d) y = 2 * 2ˣ

Answer 1

The formula for the exponential equation passing through the points (2,3) and (1,4) is y = 4ˣ.

Step-by-step explanation:

To find the formula for an exponential equation passing through the points (2,3) and (1,4), of the form y = a * bˣ, we can use the two given points to create a system of equations and solve for the values of a and b. Let's use the point (2,3) first:

1. Substitute the x and y values into the equation: 3 = a * b²
2. Next, let's use the point (1,4): 4 = a * b¹
3. Now we have a system of equations to solve:
   a * b² = 3 (Equation 1)
   a * b¹ = 4 (Equation 2)
4. Divide Equation 1 by Equation 2 to eliminate a:
   (a * b²) / (a * b¹) = 3/4
   b = 3/4
5. Substitute the value of b back into Equation 2 to find a:
   a * (3/4) = 4
   a = 16/3

Therefore, the formula for the exponential equation passing through the points (2,3) and (1,4) is y = (16/3) * (3/4)ˣ. Simplifying this, we get y = 4ˣ.