Nonlinear Regression Math 075 Summer 2016

Exponential growth 𝑦=𝑐 1+𝑎 𝑡 c = initial value a = percent increase b = 1 + a = growth factor t = time

Let’s see how this works In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. what’s the initial value? What is the percent increase? What is the growth factor? 𝑦=285 1+ .75 𝑡

Let’s see how this works You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year 1) what’s the initial value? 2) What is the percent increase? 3) What is the growth factor? 𝑦=30000 1+ .05 𝑡

Let’s see how this works The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26%. 1) what’s the initial value? 2) What is the percent increase? 3) What is the growth factor? 𝑦=6.08 1+ .0126 𝑡

Let’s see how this works The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)t where t is the number of years since 1990. What was the population in 1990? By what percent did the population increase by each year? It’s really asking for the initial value: 6191 It is increasing by 4% each year

Exponential decay 𝑦=𝑐 1−𝑎 𝑡 c = initial value a = percent increase b = 1 - a = decay factor t = time

Let’s see how this works You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. What is the equation? 1) what’s the initial value? 2) What is the percent increase? 3) What is the growth factor? 𝑦=120 1− .12 𝑡

Let’s see how this works A computer valued at $6500 depreciates at the rate of 14.3% per year. 1) what’s the initial value? 2) What is the percent increase? 3) What is the growth factor? 𝑦=6500 1− .143 𝑡