Lesson 7.2A Modeling Exponential Decay

Warm-up Write 9% as a decimal Write 11.5% as a decimal

Review Write a model to represent the number of “retweets” your tweet will have after t days if you get 10 the first day and the number triples each day after that. How much money would you have if $500 earned 6% interest compounded monthly for 10 years? Graph y = 2∙3x and y = 2∙3x+1 - 4

Exponential Decay The situation can be modeled by multiplying by some constant value, but the value is less than 1. In exponential growth we multiplied by a number greater than 1

Exponential Decay Model y = a∙bt (b < 1) or y = a(1 - r)t Compare to growth y = a∙bt (b > 1) or y = a(1 + r)t Where a is the initial value b is the decay factor r is the percent of decrease (expressed as a decimal) t is time Notice that b = 1 - r

Growth or decay? y = .7∙(3.2)t y = 100∙.8t y = 23 ∙ ( 3 4 )t

If the number of people who contact a new flu strain can be modeled by by y = 800 ∙ ( 3 5 )t, where t is the number of months since January, How many people contacted it in January? What is the decay factor? What percent decrease would this be each month? How many people will contact this flu strain in April according to this model?

If the value of a new snowmobile over time can be modeled by y = 11,500(.86)t, What is the average cost today? What is the decay factor? What is the annual percent of decrease? What would we predict the value to be in 10 years?

Write a model Use the chart of the amount of pain reliever in a patient’s bloodstream to create a model for the amount present after t hours. Then predict the amount in the bloodstream after 24 hours. Beginning 1 hour 2 hours 3 hours 500 mg 450 mg 405 mg 364.5 mg

Write a model Let’s say that in 1971 there were 4500 rare spotted zebras in the world. If there was an average decrease of 5.3% per year, how many would you expect there to be today?

Contrast Suppose you have a choice of two different jobs at graduation Start at $30,000 with a 6% per year increase Start at $40,000 with $1200 per year raise Which should you choose? One is linear growth One is exponential growth