Question

A 20-year-old university student weighs 138 lb and had a birth weight of 6 lb. Prove that at some point in her life she was growing at a rate of 6.6 pounds per year.

Solution

Verified
Step 1
1 of 2

We are told that a university student weighs 138 lbs currently and at the time of her birth she weighed 6 lbs.

The average rate of increment of her weight is

Wavg=1386200=6.6 pounds/yearW_{avg} = \dfrac{138-6}{20-0} = 6.6 \text{ pounds/year}

Now the Mean Value theorem tells us that there exists a cc between aa and bb, such that

f(c)=f(b)f(a)baf'(c) = \dfrac{f(b)-f(a)}{b-a}

In this case, we have the weight at 20 years as 138 lbs and at 0 years(approximately 1 day) as 6 lbs. Hence using the mean value theorem we should have a cc such that

f(c)=1386200=6.6 pounds/yearf'(c) = \dfrac{138-6}{20-0} = 6.6 \text{ pounds/year}

Hence this tells us that at some point the average increment shall be equal to the instantaneous increment of weight.

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Recommended textbook solutions

Biology 1st Edition by Kenneth R. Miller, Levine

Biology

1st EditionKenneth R. Miller, Levine
2,470 solutions
Nelson Science Perspectives 10 1st Edition by Christy C. Hayhoe, Doug Hayhoe, Jeff Major, Maurice DiGiuseppe

Nelson Science Perspectives 10

1st EditionChristy C. Hayhoe, Doug Hayhoe, Jeff Major, Maurice DiGiuseppe
1,359 solutions
Miller and Levine Biology 1st Edition by Joseph S. Levine, Kenneth R. Miller

Miller and Levine Biology

1st EditionJoseph S. Levine, Kenneth R. Miller
1,773 solutions
Biocalculus: Calculus for the Life Sciences 1st Edition by Day, Stewart

Biocalculus: Calculus for the Life Sciences

1st EditionDay, Stewart
5,058 solutions

Related questions