Question

Odels

Heavier birds tend to have larger wings than smaller birds. For one species of bird, the table lists the area A of the bird's wing in square inches
the bird weighs w pounds.
w (lb)
in.²)
A(w) (in.
2
150
(a) Find a function that models the data.
(b) Graph A and the data.
(c) What weight corresponds to a wing area of 500 square inches?
OA A(W) =
6
340
1+
(a) Select the correct choice below and fill in the answer boxes within your choice.
(Round to three decimal places as needed.)
10
475
14
590
18
679

Answer 1

To find a function that models the data, you need to find the relationship between the bird's weight and wing area. Since heavier birds tend to have larger wings, we can assume that the wing area is directly proportional to the weight. The function that models the data is A = 2.27W.

Step-by-step explanation:

To find a function that models the data, you need to find the relationship between the bird's weight and wing area. Since heavier birds tend to have larger wings, we can assume that the wing area is directly proportional to the weight. Let's call the weight of the bird W and the wing area A. So, the function that models the data can be represented as A = kW, where k is a constant of proportionality.

To find the value of k, we can use the given data. From the table, we can see that when the weight is 150 lbs, the wing area is 340 sq. in. Using this data point, we can set up the equation 340 = k * 150 and solve for k. Dividing both sides by 150, we get k = 2.27.

Now we have the function A = 2.27W that models the data.