1. Linear Vs. Exponential Growth
Differentiate between linear and exponential functions.

2. What is the difference between linear and exponential functions?
Linear functions
Take the form y = mx + b
Graph as a straight line
(increasing or decreasing)
Have a constant rate of change (slope)
grow by equal differences over equal intervals
(you subtract)
like arithmetic sequences x 2x 1 2 4 3 6 8 5 10 12 7 14 16 9 18 20

3. What is the difference between linear and exponential functions?
Take the form y = ax m
Graph as a smooth curve
‘growth’ = increasing
‘decay’ = decreasing
grow by equal factors / common ratio over equal intervals
(you divide)
they will get much bigger much faster!
like geometric sequences x 2x 1 2 4 3 8 16 5 32 6 64 7
128
256 9
512 10
1,024

4. Is the example linear or exponential?
Sebastian deposits $100,000 in a local bank that will pay out 5% interest every year. Is this example linear or exponential?
A certain type of corn grows at the rate of 3 inches per week. Is this example linear or exponential?
The Munn Sugar Processing Plant is able to process 10 tons of sugar per month. Assuming that this process stays steady, is this example linear or exponential?
Exercise biologist, Samantha, discovered that to reduce soreness, people should start biceps curls at 10 pounds. Then, progress weekly to 11 pounds, 14 pounds, 20 pounds, 32 pounds, 56 pounds and so on. Is this example linear or exponential?

5. Bacteria Multiplying!
This video link shows bacteria doubling every twenty minutes.
Will that be linear or exponential?
T-chart and graph of video time
T-chart and graph of real time
Time (min)
Number of Bacteria 2 20 4 40 8 60 16 80 32
100 64
120
128
140
256
160
512
180
1,024
Time (sec)
Number of Bacteria 2 1 4 8 3 16 32 5 64