Have you ever wondered how quickly the money in your bank
account will grow? For example, how much money will you have 10
years from now if you put it into a saving account?
Slide 2
In this lesson you will learn how to create and graph
exponential relationships by using a table of values
Slide 3
Lets Review Example: You start with 25 dots, and the number of
dots increase by 40% in every step. 40% growth
Slide 4
Lets Review 40% growth y = a(1+r) x y = 25(1+.4) x y = 25(1.4)
x
Slide 5
Lets Review Exponential growth Exponential decay
Slide 6
A Common Mistake If the values are growing, the growth factor
is greater than 1 y = 25(1.4) x If it is decaying, the decay factor
is less than 1 but more than 0 y = 25(.4) x
Slide 7
Core Lesson We will investigate the following: Use the
following table of values that show your bank account and number of
years to create and graph a function relating the time and money in
your account. time (years) money ($) 0100 1103 2106.09 3109.27
4112.55 5115.92
Slide 8
Core Lesson m = a(1+r) t m = (100)*(1+r) t m = (100)*1.03 t
Time (years) Money ($) 0100 1103 2106.09 3109.27 4112.55 Each term
is 3% larger than the previous term, so r=.03
Slide 9
Core Lesson time (years) money ($) time (years) money ($) 0100
1103 2106.09 3109.27 4112.55 5115.92 m = (100)*1.03 t 0 20 40 60 80
100 120 0246
Slide 10
In this lesson you have learned how to create and graph
exponential relationships by using a table of values
Slide 11
Guided Practice We will investigate the following: The
following data set shows the amount of caffeine in a persons
bloodstream after a cup of coffee; create and graph the function
that describes time and caffeine levels time (hours) caffeine (mg)
035 130.1 225.89 322.26 419.14 516.46
Slide 12
Guided Practice c = a(1+r) t c = (35)*(1+r) t c = (35)*0.86 t
time (hours) caffeine (mg) 035 130.1 225.89 322.26 419.14 516.46
Each term is 14% smaller than the previous term, so r=-.14
Slide 13
Guided Practice time (hours) caffeine (mg) time (hours)caffeine
(mg) 035 130.1 225.89 322.26 419.14 516.46 c = (35)*0.86 t 0 5 10
15 20 25 30 35 40 4.59.5
Slide 14
Extension Activities 1. Make your own exponential function,
create a table of values, and verify that the function you created
can be made from the values. 2. Use a computer and explore the
singularity concept. Investigate how exponential growth is related
to singularity. 3. Explore half-life. How is modeling half- life
similar and different to the work you have done with exponential
functions?
Slide 15
Quick Quiz 1. The population of your town increases by 1.4%
each year. If the town starts with 65,000 people, create and graph
the function that describes time and population size. 2. The number
of wolves in the Western US was in serious jeopardy for a while.
For some time, the population was decreased by 32% each year. If
the original population was 5 million, create and graph the
function describing time and wolf population.