Ryerson University

• SCIENCE 334

MCR3U Rollon Exponential Functions: Applications of Exponential Functions (U4A5) 4.5: APPLICATIONS OF EXPONENTIAL FUNCTIONS (U4A5) ● Exponential functions are appropriate models for situations in which some value constantly increases or decreases at some percentage rate or by some factor ● Some examples of situations in which exponential functions are appropriate models for include: ○ the value of an investment over a period of time ○ how much your car is worth when you trade it in ○ how long it will take before the area around Chernobyl is liveable again ○ the number of fruit flies in your kitchen since you first noticed them ● Exponential functions are in the form f(x) = ab x , where: ○ f(x) is the final value ○ a is the initial value ○ b is the growing or decaying factor THE BASE AS A PERCENT Sometimes the rate of change is expressed not as a factor but as a percent. In some cases, we express b as (1 + r) where r is the growth rate (if positive) or decay rate (if negative), expressed as a decimal (i.e., a decay rate of 2% would be written as -0.02, and b would be 0.98). Example 1: The population of a province is 35 000 in 1996 and has grown at an annual rate of 8%. What is the equation for a function that represents this growth? f(x) = a(b) x a = 35 000 b = 1 + r = 1 + 0.08 = 1.08 Therefore, the equation for this fu