GrowthDecay

8.2 Exponential Decay Goal 1: I will graph exponential decay functions. Goal 2: I will use exponential decay functions to model real-life examples.

Where is this used? Value of used cars radioactive decay Caffeine in body

Vocabulary exponential decay function: involves the equation where b is the base, and a is the initial value of y when x = 0, and b is that growth factor. y = ab x

Exponential Factors If the factor b is greater than 1, then we call the relationship exponential growth. If the factor b is less than 1, we call the relationship exponential decay.

practice Goal 1: Graph exponential decay functions State whether the function is an exponential growth or exponential decay function. growthdecay growth

Graph the function

domain: all real #s range: y > 0

Exponential Decay Models When a real-life quantity (e.g. value of car) decreases by fixed percent each time period, the amount y of the quantity after t time periods is: Where C = initial amount r = growth rate (percent written as a decimal) t = time where t  0 (1 - r) = decay factor where 1 - r < 1

Value of Car You buy a new car for $23,000. The value decreases by 15% each year. Write an exponential decay model for the car’s value. Use the model to estimate the value after 3 years.

practice An adult takes 400 mg of ibuprofen. Each hour h, the amount i of ibuprofen in the person’s system decreases by about 29%. Write an exponential decay model that describes the situation. How much is left in the system after 4 hours?

Independent Practice Suppose that 100 pounds of plutonium (Pu) is deposited at a nuclear waste site. How much of it will still be radioactive in 100,000 years? Solve graphically and algebraically.