Chapter 3 Section 2 MA1032 Data, Functions & Graphs Sidney - - PowerPoint PPT Presentation

Chapter 3 Section 2

MA1032 Data, Functions & Graphs Sidney Butler

Michigan Technological University

October 9, 2006

S Butler (Michigan Tech) Chapter 3 Section 2 October 9, 2006 1 / 6

Example

x 1 2 4 5 8 9 f (x) 4096 1024 64 16 0.25 0.0625

S Butler (Michigan Tech) Chapter 3 Section 2 October 9, 2006 2 / 6

Example

At time t = 0, a species of turtle is released into a wetland. When t = 4 years, a biologist estimates there are 300 turtles in the wetland. Three years later, the biologist estimates there are 450 turtles. Let P represent the size of the turtle population in year t.

1 Find a formula for P = f (t) assuming linear growth. Interpret the

slope and P-intercept of your formula in terms of the turtle population.

2 Now find a formula for P = g(t) assuming exponential growth.

Interpret the parameters of your formula in terms of the turtle population.

3 In year t = 12, the biologist estimates that there are 900 turtles in the

• wetland. What does this indicate about the two population models?

S Butler (Michigan Tech) Chapter 3 Section 2 October 9, 2006 3 / 6

Problem #28

Suppose f (−3) = 5

8 and f (t) = 20. Find a formula for f assuming it is:

1 Linear 2 Exponential S Butler (Michigan Tech) Chapter 3 Section 2 October 9, 2006 4 / 6

Comparing Growth Rates

1 2 3 4 5 6 7 8 9 1 10 20 30 40 50 60 70 80

y=5x+20 y=3(1.08)^x

S Butler (Michigan Tech) Chapter 3 Section 2 October 9, 2006 5 / 6

Summary

1 Determining linearity 2 Determining exponentials 3 Exponential Formulas S Butler (Michigan Tech) Chapter 3 Section 2 October 9, 2006 6 / 6