After discussing the graph, explain characteristics of exponential functions to the students.
Exponential Function: A function that involves the expression bx where the base b is a positive number other than 1
Asymptote: A line that a graph approaches as you move away from the origin
Exponential Growth Function: A function of the form f(x)=abx where a>0 and b>1
Growth Factor: The quantity 1+r in the exponential growth model y=a(1+r)t where a is the initial amount and r is the percent increase expressed as a decimal
Compound Interest: Consider an initial principal P deposited in an account that pays interest at an annual rate r, compounded n times per year. The amount A in the account after t years can be modeled by the equation
Exponential Decay Function: A function of the form f(x)=abx where a>0 and 0<b<1
Decay Factor: The quantity 1-r in the exponential growth model y=a(1-r)t where a is the initial amount and r is the percent decrease expressed as a decimal