1. Exponential Growth and Decay

2. Essential Question
How does exponential growth differ from exponential decay and how do I find the rate of change?

3. Exponential Functions
An exponential function has an x in the exponent (and numerical values everywhere else).
y = a•bx
Coefficient: a
Base: b
Exponent: x

4. The base determines growth or decay.
Put y = 3(2)x into y1 in your calculator and graph.
Does it look like it will be growth or decay? Why? Share with a partner.
It is growth because as x values increase, y values also increase.
What is the b value (base) in this equation? 2

5. Now put y = 3(1/2)x into y1 in your calculator and graph.
Does it look like it will be growth or decay? Why? Share with a partner.
It is decay because as x values increase, y values decrease.
What is the b value (base) in this equation?
1/2

6. So…….
If the base “b” is greater than 1, the function will be exponential growth.
If the base “b” is less than 1 (but always greater than 0), the function will be exponential decay.

7. On your whiteboard: (((Remember: y = a•bx)))
y = 5x
a = _____ (y-intercept)
b = _____ (base value)
Growth or decay? _________ 1 5
growth

8. On your whiteboard: (((Remember: y = a•bx)))
y = (0.4)x
a = _____ (y-intercept)
b = _____ (base value)
Growth or decay? _________ 1
0.4
decay

9. On your whiteboard: (((Remember: y = a•bx)))
y = 8(0.25)x
a = _____ (y-intercept)
b = _____ (base value)
Growth or decay? _________ 8
0.25
decay

10. On your whiteboard: (((Remember: y = a•bx)))
y = 4(2.5)x
a = _____ (y-intercept)
b = _____ (base value)
Growth or decay? _________ 4
2.5
growth

11. On your whiteboard: (((Remember: y = a•bx)))
y = 1/2(3)x
a = _____ (y-intercept)
b = _____ (base value)
Growth or decay? _________
1/2 3
growth

12. On your whiteboard: (((Remember: y = a•bx)))
y = 50(1.01)x
a = _____ (y-intercept)
b = _____ (base value)
Growth or decay? _________ 50
1.01
growth

13. Finding the rate of growth or decay
A = C(1 ± r)x
How can we write 3 as 1 ± r and what would r be?
Well, 3 = 1+2 so r = 2
We say this function is growing at a rate of 200%.
How can we write 0.6 as 1 ± r and what would r be?
Well, 0.6 = 1 – 0.4 so r = 0.4
We say this function is decaying at a rate of 40%. a b

14. Socrative