Final answer:
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:
- y: represents the dependent variable (the output)
- a: represents the initial value (the y-intercept)
- e: represents the base of the natural logarithm (approximately equal to 2.7183)
- b: represents the growth/decay factor (the rate at which the function increases or decreases over time)
- 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.