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 65 kilograms. (note: 65 kilograms is approximately 143 pounds.)
( b(w)=) calories (round to the nearest calorie as needed.)

Explanation:

Step1: Substitute \( w = 65 \) into the function

Given \( B(w)=70w^{\frac{3}{4}} \), when \( w = 65 \), we have \( B(65)=70\times65^{\frac{3}{4}} \).
First, calculate \( 65^{\frac{3}{4}}=(65^{\frac{1}{4}})^3 \).
We know that \( 65^{\frac{1}{4}}=\sqrt[4]{65}\approx2.8 \) (using a calculator, \( 65 = 5\times13 \), \( \sqrt[4]{65}\approx2.8 \)), then \( (65^{\frac{1}{4}})^3\approx2.8^3 = 21.952 \).
Another way is to use the formula \( a^{\frac{m}{n}}=\sqrt[n]{a^m} \), so \( 65^{\frac{3}{4}}=\sqrt[4]{65^3}=\sqrt[4]{274625}\approx21.952 \).

Step2: Calculate \( B(65) \)

Now, \( B(65)=70\times21.952 \).
\( B(65)=70\times21.952 = 1536.64\)

Answer:

\(1537\) calories