The table below gives the population rank x and the estimated population y (in hundred thousands) for the five most populated bacteria colonies in a lab. 8,053 2 2,940 3 2,000 1,480 1,224 Find an equation of the power function that models the data, and predict the population of the sixth most populous bacteria colony.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Population Data of Bacteria Colonies in a Lab

The table below presents the population rank \( x \) and the estimated population \( y \) (in hundred thousands) for the five most populous bacteria colonies in a lab.

| Rank (x) | Population (y) |
|----------|----------------|
| 1        | 8,053          |
| 2        | 2,940          |
| 3        | 2,000          |
| 4        | 1,480          |
| 5        | 1,224          |

#### Objective
Find an equation of the power function that models the data and predict the population of the sixth most populous bacteria colony.

---

In order to find the power function that best fits the given data, one can use regression techniques. The power function can generally be expressed in the form:

\[ y = a \cdot x^b \]

Where \( a \) and \( b \) are constants to be determined. Once the constants are calculated, we can use the equation to predict the population of the sixth most populous bacteria colony (i.e., when \( x = 6 \)).
Transcribed Image Text:### Population Data of Bacteria Colonies in a Lab The table below presents the population rank \( x \) and the estimated population \( y \) (in hundred thousands) for the five most populous bacteria colonies in a lab. | Rank (x) | Population (y) | |----------|----------------| | 1 | 8,053 | | 2 | 2,940 | | 3 | 2,000 | | 4 | 1,480 | | 5 | 1,224 | #### Objective Find an equation of the power function that models the data and predict the population of the sixth most populous bacteria colony. --- In order to find the power function that best fits the given data, one can use regression techniques. The power function can generally be expressed in the form: \[ y = a \cdot x^b \] Where \( a \) and \( b \) are constants to be determined. Once the constants are calculated, we can use the equation to predict the population of the sixth most populous bacteria colony (i.e., when \( x = 6 \)).
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