1. Transformation Interest problems Half life
3.1 Exponential Function
Transformation
Interest problems
Half life

2. Exponential Function f(x) = ax a > 0 and a ≠ 1
x is any real number.
Notice 20 = 1
Any number to the zero power
(except 0) equals 1

3. What if there is x is a negative number
We would have a decreasing exponential function

4. What is the horizontal asymptote?
We would have a decreasing exponential function

5. Transformations (shifts happen)
y = 4x y = 4x + 3

6. Now a little to the right
y = 4x y = 4(x – 3)

7. Reflect across the y axis
y = 4x y = 4-x

8. Lets use a different base
What do you see?

9. How about the base e e ≈ 2.71828 ……… it is transcendental. e ≈
Just another base that most natural event follow

10. Base 10 is also common, that it is on your calculators

11. Continuous Compounding Interest uses e
Now for my favorite equation.
Pert P is for principle
r is for Rate
t is for Time
$4000 at 8% interest for 10 years at continuous compounding interest.
4000e(.08)(10) =

12. Continuous Compounding Interest uses e
Now for my favorite equation.
Pert P is for principle
r is for Rate
t is for Time
$4000 at 8% interest for 10 years at continuous compounding interest.
4000e(.08)(10) = $

13. Compounding a number of times per year equation
Amount =
N is the number of times per year
Quarterly is 4
Semi Annual is 2
Monthly is 12

14. Decay function In a decay function a (the base) is 0 < a< 1
In other words a fraction
The most famous is half life, where a is ½.
h is half life
P initial amount
A is remaining
amount

15. Homework
Page 206 – 208
# 2, 7, 13, 21,
33, 43, 47,
51, 54, 57,
61, 67

16. Homework
Page 206 – 208
# 4, 10, 17, 27,
37, 45, 49,
53, 55, 58,
62, 78