To find the function that gives the length L as a function of its mass m, we need to solve the equation m(L) = 0.00001L^3 for L.
0.00001L^3 = m
Taking the cubed root of both sides, we get:
L^3 = (m/0.00001)
L = (m/0.00001)^(1/3)
So, the function that gives the length L in centimeters of a red snapper as a function of its mass m in kilograms is:
L(m) = (m/0.00001)^(1/3)
Now, we need to find the length of a four-year-old snapper that weighs about 1.5 kilograms.
So we plug in m = 1.5 into the function:
L(1.5) = (1.5/0.00001)^(1/3)
L(1.5) = 150000^(1/3)
Using a calculator to find the cube root of 150000, we get:
L(1.5) ≈ 53.164
Rounding to the nearest whole number, the length of a four-year-old snapper that weighs about 1.5 kilograms is 53 centimeters.
The function m(L)=0.00001L^3 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.
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