Question

marina silva, in the journal of mammalogy (1998), gives the following formula for the approximate body length of mammals based on the mammals b
ss
l ( m ) = 0.330 sqrt 3 { m }
ere ( l ( m ) ) represents the body length in meters of a mammal with a body mass of ( m ) kilograms.
(a) use this model to estimate the body length of a mammal with a body mass of ( 5.1 mathrm { kg } ). (include units with your numerical answer. round your
answer to two decimal places.)
the length of a mammal with a body mass of ( 5.1 mathrm { kg } ) will be ( 0.57 ) meters
(b) use this model to estimate the body length of a mammal with a body mass of ( 21 mathrm { kg } ). (include units with your numerical answer. round your
answer to two decimal places.)
the length of a mammal with a body mass of ( 21 mathrm { kg } ) will be ( 0.91 ) meters
(c) if this model is valid for mammals with body masses between ( 0.01 ) and ( 250 mathrm { kg } ), including ( 0.01 ) and ( 250 mathrm { kg } ), what is the models range?
( 0.07,2.08 )
( 0.07,2.15 )
( ( 0.01,250 ) )
( ( 0.07,2.08 ) )
( 0.01,250 )
(d) estimate numerically the body mass of a mammal with a body length of 2 meters. (include units with your numerical answer. round your answer
to two decimal places.)
the body mass of a mammal with a body length of 2 meters is ( 222.52 mathrm { kg } )

Explanation:

Step1: Substitute \( L = 2 \) into the formula \( L(M)=0.330\sqrt[3]{M} \)

We get \( 2 = 0.330\sqrt[3]{M} \).

Step2: Solve for \( \sqrt[3]{M} \)

Divide both sides by \( 0.330 \): \( \sqrt[3]{M}=\frac{2}{0.330}\approx6.0606 \).

Step3: Solve for \( M \)

Cube both sides: \( M=(6.0606)^{3}\approx223.09 \).

Answer:

\( 223.09\space kg \)