Suppose that the surface area S of a bird's wings in square feet can be modeled by S(w) = 1.27w^2/3, where w is the weight of the bird in pounds, with 1
The surface area of a bird's wings can be modeled by the equation S(w) = 1.27w^(2/3), where w is the weight of the bird in pounds.
To find the surface area when the bird weighs 1 pound, we substitute w = 1 into the equation:
S(1) = 1.27(1)^(2/3)
S(1) = 1.27(1)
S(1) = 1.27
Therefore, the surface area of the bird's wings when it weighs 1 pound is 1.27 square feet.
To find the weight of the bird when the surface area of its wings is 1.5 square feet, we can plug in this value into the equation S(w) = 1.27w^(2/3) and solve for w.
Given:
S(w) = 1.5 square feet
Substituting into the equation:
1.5 = 1.27w^(2/3)
To isolate w, we need to isolate w^(2/3) first. Divide both sides of the equation by 1.27:
1.5 / 1.27 = w^(2/3)
Performing the division:
1.181 = w^(2/3)
Now, to solve for w, we need to cube both sides of the equation to get rid of the exponent. Raise both sides to the power of 3:
(1.181)^(3) = (w^(2/3))^(3)
Taking the cube:
1.181^3 = w^2
Calculating 1.181^3:
1.181^3 = 1.637
Now we can solve for w by taking the square root of both sides:
√(1.637) = √(w^2)
Taking the square root:
1.28 = w
Therefore, the weight of the bird when the surface area of its wings is 1.5 square feet is approximately 1.28 pounds.