Question

basal metabolic rate (bmr) is the number of calories per day a person needs to maintain life. a persons basal metabolic rate b(w) in calories per day can be estimated with the function b(w)=70w^\frac{3}{4}, where w is the persons weight in kilograms.
estimate the bmr for a person who weighs 63 kilograms. (note: 63 kilograms is approximately 139 pounds.)
b(w)=\square calories (round to the nearest calorie as needed.)

Explanation:

Step1: Substitute \( w = 63 \) into the formula

Given \( B(w)=70w^{\frac{3}{4}} \), when \( w = 63 \), we have \( B(63)=70\times63^{\frac{3}{4}} \).
First, find \( 63^{\frac{3}{4}}=(63^{\frac{1}{4}})^3 \).
We know that \( 63 = 3^2\times7 \).
\( 63^{\frac{1}{4}}=\sqrt[4]{63}\approx2.785 \) (using a calculator for the fourth - root of 63).
Then \( (63^{\frac{1}{4}})^3\approx2.785^3\approx21.57 \).

Step2: Calculate \( B(63) \)

Now, \( B(63)=70\times21.57 = 1510 \) (rounded to the nearest calorie).

Answer:

1510