Page 765 - Algebra 1

E x p o n e n t i a l g r o w t h i s m o d e l e d b y t h e f u n c t i o n f (x) = k b x , w h e r e k > 0 . The percent of growth b, expressed as a decimal number, is greater than 1.
Exploration Analyzing Different Values of k in the Exponential Growth Function
Step 1: Take one sheet of notebook paper. Fold it in half. Unfold the paper and count the number of rectangular regions formed. Record the number of folds and regions in a table like the one below.
Materials
• several sheets of notebook paper
Folds
Regions
0
1
1
2
2
3
4
Refold the paper along the initial crease you made and fold it in half again. Continue counting regions and folding in half at least four times.
Step 2: Take three sheets of notebook paper and stack them. Repeat Step 1. Create and complete a table like the one below.
Step 3: Take five sheets of notebook paper and stack them. Repeat Step 1. Create and complete a table like the one below.
Folds
Regions
0
3
1
6
2
3
4
Folds
Regions
0
5
1
2
3
4
Math Reasoning
Analyze Why are each of the three functions named using function notation?
7. Plot the points on one coordinate plane. Let x = the number of folds. Let y = the number of regions. Connect the point for each set of data with a smooth curve.
The data in the Exploration are included in the graphs of the functions f(x) = 2x, g(x) = 3(2)x, and h(x) = 5(2)x, respectively. All three functions are of the form y = k(b)x.
8. What is the y-intercept of each function? Compare the y-intercept of each e qu at ion t o y = k b x . Na m e t h e y -i nt e r c e pt of y = k b x .
750 Saxon Algebra 1