1. MAT 142 Lecture Video Series

2. Exponential Growth and Decay
Right Triangle Trigonometry (MAT 142)
Exponential Growth and Decay

3. Right Triangle Trigonometry (MAT 142)
Objectives
Solve applications problems involving exponential growth and decay.

4. Basic Growth/Decay Function
Right Triangle Trigonometry (MAT 142)
Basic Growth/Decay Function
a is the initial amount (f(0))
k is the relative growth rate
t is time

5. Basic Growth/Decay Function
Right Triangle Trigonometry (MAT 142)
Basic Growth/Decay Function
the function grows if k > 0
the function decays if k < 0
the inverse of the function is used to find time t and relative growth rate k

6. Right Triangle Trigonometry (MAT 142)
The fox population in a certain region has a relative growth rate of 4% per year. It is estimated that the population in the year 2000 was 5000.
Find a function that models the population t years after 2000
(t = 0 for 2000).
Use the model to estimate the fox population in 2008.

7. Right Triangle Trigonometry (MAT 142)
The number of bacteria in a culture is given by the function where t in measured in hours.
What is the relative growth rate of the bacteria population?
What is the initial population of the culture?
How many bacteria will the culture contain in 5 hours?

8. Right Triangle Trigonometry (MAT 142)
A bacteria culture initially contains 1500 bacteria and doubles every half hour. The formula for the population is for some constant k.
Find the size of the bacterial population after 20 minutes.
Find the size of the bacterial population after
9 hours.

9. Right Triangle Trigonometry (MAT 142)
If $2000 is invested in a bank account at an interest rate of 4% per year, compounded continuously, how many years will it take for your balance to reach $40000?

10. Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2010 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University