Question

The function m(L)=0.00001L₃ gives the mass m in kilograms of a red snapper of length L centimeters. Determine the function that gives the length L in centimeters of a red snapper as a function of its mass m in kilograms. Then find the length of a four-year-old snapper that weights about 1.5 kilograms. Round to the nearest whole number.

A. The function is L(m)=³√100,000m. The length of a four-year-old snapper that weights about 1.5 kilograms is about 74 centimeters.
B. The function is L(m)=³√10,000m. The length of a four-year-old snapper that weights about 1.5 kilograms is about 34 centimeters.
C. The function is L(m)=³√10,000m. The length of a four-year-old snapper that weights about 1.5 kilograms is about 25 centimeters.
D. The function is L(m)=³√100,000m. The length of a four-year-old snapper that weights about 1.5 kilograms is about 53 centimeters.

Answer 1

The function that gives the length L in centimeters of red snapper as a function of its mass m in kilograms is L(m) = ³√(m/0.00001). The length of a four-year-old snapper that weighs about 1.5 kilograms is about 53 centimeters.

Step-by-step explanation:

To determine the function that gives the length L in centimeters of red snapper as a function of its mass m in kilograms, we need to solve the given function for L. The given function is m(L) = 0.00001L₃. To find L(m), we can rewrite the equation as L = ³√(m/0.00001).

Now, let's find the length of a four-year-old snapper that weighs about 1.5 kilograms. Using the function L(m) = ³√(m/0.00001), we substitute 1.5 for m:

L(1.5) = ³√(1.5/0.00001) = ³√150,000 ≈ 53 centimeters.

So, the function that gives the length L in centimeters of red snapper as a function of its mass m in kilograms is L(m) = ³√(m/0.00001). The length of a four-year-old snapper that weighs about 1.5 kilograms is about 53 centimeters.