Problem 2. The table below gives the expected growth rate, g(t), in ounces per w

Question

Problem 2. The table below gives the expected growth rate, g(t), in ounces per week, of the weight of a baby in its first 54 weeks of life. Assume for this problem that g(t) is a decreasing function.

Week t 0 9 18 27 36 45 54

growth rate g(t) 6 6 4.5 3 3 3 2

a. Using six subdivisions, find an overestimate and underestimate for the total weight gained by a baby over its first 54 weeks of life.

b. How frequently over the 54 week period would you need data for g(t) to be measured to find overestimates and underestimates for the total weight gain over this time period that differ by 0.5 lb (8 oz)? (See the handout on Estimating Error in Riemann Sums)

Explanation / Answer

A) the function is decreasing so the left hand sum will be over estimate , right hand sum will be under estimate

left sum =9*(6+ 6+ 4.5+ 3+ 3 +3) =229.5oz

right sum = 9*(6+ 4.5+ 3+ 3 +3+2) =193.5oz

the weight to be between 12 and 14 lb

b) difference between over and under estimates is 8=[g(54)-g(0)]t

8=[6-2]t

t=2weeks

we need data every 2 weeks

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