Example 3
The table shows the number of bacteria in a culture after the given number of hours. Find a good model for the data. Based on the model, how many bacteria will be in the culture after an additional ten hours?
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Step 1 Press
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Step 2 Notice from the scatter plot that the data appears exponential. Find the equations for the best-fitting exponential function. Press
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Step 3 Graph the function. Press
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Step 4 In 10 more hours, there will be approximately
| Hour | Bacteria |
|---|---|
| 1 | 2205 |
| 2 | 2270 |
| 3 | 2350 |
| 4 | 2653 |
| 5 | 3052 |
| 6 | 3417 |
| 7 | 3890 |
| 8 | 4522 |
| 9 | 5107 |
| 10 | 5724 |
Exercises
Use a graphing calculator to find the exponential or quadratic function that best fits each set of data. Graph each function.
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x y 4.9 0 3.8 1 5.0 2 8.1 3 13.3 4 70.2 -
x y 0.1 0.4 1 1.6 3 6.4 5 25.6 7 102.4 -
x y 1 3.5 2 2.11 3 1.30 4 0.73 5 0.28 6 0.08 -
x y 0.04 0 0.1 1 0.5 2 2.5 3 12.5 4 62.5 - Writing In Exercise 6 the function appears to level off. Explain why.
- Find a quadratic model for the data in Exercise 6. Compare the graphs of the quadratic and exponential models for this data. Predict the y-values for both models when
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions