Question

Which of the following formulas can be used to determine an exponential function from two given points (x₁, y₁) and (x₂, y₂)?

a) y = aeᵇˣ
b) y = aˣ + b
c) y = abˣ
d) y = a + bx

Answer 1

To determine an exponential function from two given points (x₁, y₁) and (x₂, y₂), you can use the formula y = aeᵇˣ, where a is the initial value, e is the base of the natural logarithm, b is the growth/decay factor, and x is the independent variable.

Step-by-step explanation:

The formula to determine an exponential function from two given points (x₁, y₁) and (x₂, y₂) is:

a) y = aeᵇˣ

Let's break down the formula:

1. y: represents the dependent variable (the output)
2. a: represents the initial value (the y-intercept)
3. e: represents the base of the natural logarithm (approximately equal to 2.7183)
4. b: represents the growth/decay factor (the rate at which the function increases or decreases over time)
5. x: represents the independent variable (the input)

By plugging in the values of the two given points into the equation, you can solve for the variables a and b. This will give you the specific exponential function that passes through those two points.