Warm Up Homework: Exponential Growth & Decay Worksheet Warm-Up: Solve by factoring: 2x2 – 6x + 4 = 0

Warm-Up Solve by factoring: 2x2 – 6x + 4 = 0

HW Review

Exponential Growth or Decay What do you think is the difference between exponential growth and exponential decay?

Exponential Growth or Decay?

Exponential Growth or Decay?

Exponential Growth

Identify the initial amount a and the growth factor b in each exponential function. f (x) = 3 · 5x y = 250 · 1.065x g(t) = 3.5t h(x) = 5 · 1.02x

Exponential Growth Identify the original amount and the growth factor in the exponential function

Exponential Growth 100% represents the original number, and you need to make that number “grow” by ___%. What is 100% as a decimal? For example, how could we show 14% growth?

Example 1 A town has 8496 people. The population is increasing at a rate of 3.5% per year. How many people will there be in 5 years? a = b = x =

Example 2 A population of rabbits doubles every six months. Assume that you begin with 8 rabbits. How many rabbits will there be after 4 years? a = b = x =

Example 3 A population of 24,500 people has been increasing at a rate of 1.025% per year. What will be the population in 15 years if growth continues at this rate?

Example 4 The town manager reports that revenue for a given year is $2.5 million. The budget director predicts that revenue will increase by 4% per yr. If the director’s prediction holds true, how much revenue will the town have available 10 years from the date of the town manager’s report?

Exponential Decay How would you show 15% decay?

Identify the initial amount a and the decay factor b in each exponential function. y = 8 · 0.8x f (x) = 12 · 0.1x

Example 5 The half life of a radioactive substance is the length of time it takes for half of the substance to decay into another substance. Radioactive iodine is used to treat some forms of cancer. The half life of iodine-131 is 8 days. A patient receives a 12mCi (millicuries) treatment. How much iodine 131 is left in the patient 16 days later? 16 days = 2 half lives a = ? b = ? x = ?

Example 6 In 1980, the population of a town was 17,000. The population has been decreasing at a rate of 1.4% per year. At that rate, what will the population of the town be in 1990? a = ? b = ? x = ?

Example 7 The half-life of a certain substance is 4 days. If you have 100 g of the substance, how much will be left after 12 days?

Example 8 The value of a $1750 computer decreases 30% annually. What will be the value of the computer after 3 years?

State whether the equation represents exponential growth, exponential decay, or neither. y = 0.82 · 3x f (x) = 5 · 0.3x f (x) = 18 · x2 y = 0.9x