1. Nonlinear Regression
Math 075 Summer 2016

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

3. 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
what’s the initial value?
What is the percent increase?
What is the growth factor?
𝑦= 𝑡

4. Let’s see how this works
You have inherited land that was purchased for $30,000 in 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= 𝑡

5. 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= 𝑡

6. 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 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

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

8. 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

9. 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= − 𝑡