Vocabulary
Exponential decay function- If a>0 and 0<b<1, then the function y=ab^x is an exponential decay function with decay factor b.
Decay factor- The quantity b in the exponential decay function y=ab^x with a>0 and 0<b<1.
Decay factor- The quantity b in the exponential decay function y=ab^x with a>0 and 0<b<1.
Exponential decay functions have the form y=ab^x where a>0 and 0<b<1. The base of an exponential decay function is called the decay factor.
Parent Function for Exponential Decay Functions
The function f(x)=b^x, where 0<b<1, is the parent function for the family of exponential decay functions with base b.
Parent Function for Exponential Decay Functions
The function f(x)=b^x, where 0<b<1, is the parent function for the family of exponential decay functions with base b.
Transformations
The graph of a function y=ab^x is a vertical stretch or shrink of the graph of y=b^x, and the graph y=ab^(x-h) +k is a translation of the graph of y=ab^x.
The graph of a function y=ab^x is a vertical stretch or shrink of the graph of y=b^x, and the graph y=ab^(x-h) +k is a translation of the graph of y=ab^x.
Exponential Decay Models
When a real-life quantity decreases by a fixed percent each year (or other time period), the amount y of the quantity after t years can be modeled by the equation:
y=a(1-r)^t
where a is the initial amount and r is the percent decrease expressed as a decimal. The quantity 1-r is the decay factor.
When a real-life quantity decreases by a fixed percent each year (or other time period), the amount y of the quantity after t years can be modeled by the equation:
y=a(1-r)^t
where a is the initial amount and r is the percent decrease expressed as a decimal. The quantity 1-r is the decay factor.