Growth & Decay If the common ratio is greater than 1, (r>1) f (x) = f(0)r x has a graph that goes up to the right and is increasing or growing. If 0 < r < 1, f (x) = f(0)r x has a graph that goes down to the right and is decreasing or decaying.

GrowthDecay r> 10<r<1

Anything that grows or decays exponentially, grows or decays by a fixed percent. For exponential growth, the rate of change increases with time – it grows faster and faster. For exponential decay, the rate of change decreases with time - the decaying slows down.

Examples of exponential growth: *populations (rabbits) *bacteria and viruses *credit payments *investments increasing in value Examples of exponential decay: *radioactive substances *investments losing value *metabolism of some medicines *value of objects Many real world situations can be modeled by exponential functions.

For exponential growth, we use the formula f(t) = f(0)(1 + r) t f(x) is final amount, f(0) is initial amount, r is the percent of change expressed as a decimal, and t is the number of time intervals. Why do we use (1+r)?

Make a table, write an equation and graph. ______________ has a population of ________ The population is growing at a rate of ________. How many people will live in... 1 year? 5 years? 10 years? 50 years?

A college’s tuition has risen 5% each year since If the tuition in 2000 was $10,850, write an equation for the amount of the tuition t years after What is the tuition 2010? What will tuition be in 2016?

For exponential decay, we use the formula f(x) =a(1 - r) t f(x) is final amount, a is initial amount, r is the percent of change expressed as a decimal, and t is the number of time intervals.

During an economic recession, a charitable organization found that its donations dropped by 1.1% per year. Before the recession, its donations were $390,000. Write an equation to represent the charity’s donations since the beginning of the recession. Estimate the amount of donations 5 years after the start of the recession.