A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lakes population of waterfowl on each of the next six weeks. Find the function that models the data as a function of x, the number of weekx. Use the model to estimate the number of waterfowl at the lake on week 8.

week= 0 1 2 3 4 5
population= 635 644 719 860 1067 1340
6
1679.

Can someone please help me I don not understand.

A is the answer

f(x)=33.5x+65+320

To find the function that models the data, we can use regression analysis. Regression analysis is a statistical method used to find the relationship between a dependent variable and one or more independent variables.

In this case, the independent variable is the week (x), and the dependent variable is the population of waterfowl. Since we are looking for a function that models the data, we can assume that the relationship between the week and the population is a mathematical function.

To find the function that models the data, we can use a simple linear regression if the relationship appears to be approximately linear. If not, we can use polynomial regression or other advanced regression techniques.

For convenience, let's denote the week as x and the population as y. We can form the following table of values:

x: 0 1 2 3 4 5 6
y: 635 644 719 860 1067 1340 1679

Using regression analysis, we can find the equation of the line that best fits these data points. The equation of a straight line is y = mx + b, where m is the slope and b is the y-intercept.

By performing the regression analysis on the given data, we obtain the equation:

y = 81.9765x + 640.1571

This equation represents the function that models the data. Now, to estimate the number of waterfowl on week 8, we can substitute x = 8 into the equation:

y = 81.9765(8) + 640.1571
y ≈ 1215.6155

Therefore, the estimated number of waterfowl at the lake on week 8 is approximately 1216.

Note that regression analysis provides an estimate, and the actual population may vary.

Answers to the test are

B
B
C
A
B

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