1. 7.1 – Exploring Exponential Models

2. Harry Potter and the Deathly Hallows Part II
VIDEO 

3. The Gemino Curse
When Hermione touches the bracelet, after one second it multiplies by 5. Then, after another second, each of those multiply by 5...
x y 1 2 3 4
Can you write a function to express this?

4. y = abx This is called an exponential function.
An exponential function is a function with the general form:
y = abx
where a ≠ 0 b > 0, b ≠ 1.

5. if a > 0 and b > 0, the function represents exponential growth.
y = abx
if a > 0 and b > 0, the function represents exponential growth.
if a > 0 and 0 < b < 1, the function represents exponential decay.

6. For both growth and decay:
the y-intercept is (0, a)
the domain is all real numbers
the asymptote is y = 0
the range is y > 0

7. Can we graph the Gemino Curse function?

8. Ex 1: Identify whether y = 2(3)x is exponential growth or decay and graph.
b =
Growth or Decay?

9. Ex 1: Identify whether y = 12(0
Ex 1: Identify whether y = 12(0.5)x is exponential growth or decay and graph.
a =
b =
Insert graph here
Growth or Decay?

12. You can also model growth and decay with the function…
A(t) = a(1 + r)t
For exponential growth, b > 1 is the growth factor. The quantity increases by a constant percentage each time period.
For exponential decay, 0 < b < 1 is the decay factor. The quantity decreases by a constant percentage each time period.

13. A(t) = a(1 + r)t
For exponential growth, the percentage increase r is the rate of increase or growth rate and b = 1 + r.
For exponential decay, the percentage increase r is the rate of decay. Usually rate of decay < 0, so b = 1 + r.
r will need to be written as a decimal
(Ex: 40% = 0.4)

14. growth (r > 0) or decay
Rate of
growth (r > 0) or decay
(r < 0)
Amount
after t time periods
A(t) = a(1 + r)t
Initial
amount
Number
of time periods

15. Ex: You invested $1000 in a savings account at the end of 6th grade
Ex: You invested $1000 in a savings account at the end of 6th grade. The account pays 5% annual interest. How much money will be in the account after 6 years?
A(t) =
t =
r =
a =

16. Ex: In 2003 there were 150 Iberian lynx, in 2004 there were only 120
Ex: In 2003 there were 150 Iberian lynx, in 2004 there were only 120. If this trend continues and the population is decreasing exponentially, how many Iberian lynx will there be in 2014?
A(t) =
t =
r =
a =

17. Homework
Worksheet questions