Biologist have have found that the weight W of a bird and the length L of it’s wing span are related by L=kW1/3, where k is a constant. The following list L and W for one species of bird. What is the value of k?
W kilograms0.1 0.4 0.8 1.1
L meters 0.399 0.634 0.798 0.888
To find the value of k in the equation, we need to use the given data points and solve for k.
The equation relating the weight W and the length L is given as L = kW^(1/3), where k is the constant.
Given data points are:
W = (0.1, 0.4, 0.8, 1.1) kilograms
L = (0.399, 0.634, 0.798, 0.888) meters
We can substitute the values of W and L into the equation for each data point and solve for k:
For the first data point (W = 0.1 kilograms, L = 0.399 meters):
0.399 = k(0.1)^(1/3)
Raise both sides to the power of 3 to eliminate the cube root:
(0.399)^3 = k(0.1)
Simplifying:
0.06354 = 0.1k
Now, divide both sides of the equation by 0.1 to solve for k:
k = 0.06354 / 0.1
k = 0.6354
Therefore, the value of k in the equation L = kW^(1/3) is approximately 0.6354.