Math Tutoring on Graphing Exponential Functions
An Exponential Function is a function in the form: f (x) = abᵡ, where ‘a’ can't be equal to zero, ‘b’ must be greater than zero and ‘b’ can't be equal to one. If ‘a’ was equal to zero or ‘b’ was equal to one, we would have a Constant Function, not an exponential function. The value of ‘a’ is called the Initial Value or Starting Value which is the function value when the input ‘x’ is equal to zero and therefore ‘a’ also gives us the Vertical Intercept which would be the ordered pair, ( 0, a).The base ‘b’ is called the Growth Factor or Decay Factor.
b = 1 + r, where r is equal to the growth rate per unit of time as a decimal. So if the base ‘b’ is greater than one, then ‘r’, the growth rate, would have to be greater than zero or positive, and therefore the function represents exponential growth which is the function increasing at a constant percentage with a growth rate of ‘r’. Now if the base ‘b’ is between zero and one, that means ‘r’ the growth rate would be negative, or less than zero, and therefore the function represents exponential decay which is the function decreasing at a constant percentage and the decay rate is equal to the opposite value of ‘r’.
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1. What is an Exponential Function?
2. What is known as Initial Value?
3. What is Growth Factor?
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