The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation $F = 0.4 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 400 lb of food per day.
A) 15,000 lb
B) $20,000 \mathrm { lb }$
C) $10,0001 \mathrm {~b}$
D) 5,000 $1 \mathrm {~b}$
E) none of these

Question

The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation $F = 0.4 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 400 lb of food per day. 
A) 15,000 lb
B) $20,000 \mathrm { lb }$
C) $10,0001 \mathrm {~b}$
D) 5,000 $1 \mathrm {~b}$
E) none of these

Quizplus · Accepted Answer

We have the equation 
$$F=0.4x^{3/4}$$
We are given that an elephant consumes 400 lb of food per day, so we can plug this into our equation and solve for x:
$$400=0.4x^{3/4}$$
$$1000=x^{3/4}$$
$$\log_{10} 1000 = \log_{10} x^{3/4}$$
$$3 = \frac{3}{4} \log_{10} x$$
$$x = 10^{4}$$
Therefore, the weight of the elephant is 10,000 lb, which is answer choice C.

The Average Daily Food Consumption F of a Herbivorous Mammal F=0.4x3/4F = 0.4 x ^ { 3 / 4 }F=0.4x3/4

The Average Daily Food Consumption F of a Herbivorous Mammal $F = 0.4 x ^ { 3 / 4 }$