Newborn blue whales are approximately 24 feet long and weigh 3 tons. Young whale
ID: 3031201 • Letter: N
Question
Newborn blue whales are approximately 24 feet long and weigh 3 tons. Young whales are nursed for 7 months, and by the time of weaning they often are 53 feet long and weigh 20 tons. Let L and W denote the length (in feet) and the weight (in tons), respectively, of a whale that is t months of age.
(a) If L and t are linearly related, express L in terms of t. L(t) = c
(b) What is the daily increase in the length of a young whale? (Use 1 month = 30 days. Enter your answer as a fraction.) ft/day
(c) If W and t are linearly related, express W in terms of t. W(t) = c
(d) What is the daily increase in the weight of a young whale? (Enter your answer as a fraction.) ton/day
Explanation / Answer
a)
at t= 0 , L = 24
at t=7, L = 53
(L(t) - 24)/(t-0) = (53-24)/(7-0)
L(t) - 24 = t*29/7
L(t) = (29/7)*t + 24
b)
slope = 29/7 feet /month
daily increase = (29/7*30) feet/day
=29/210 ft/day
c)
at t= 0 , W = 3
at t=7, W = 20
(W(t) - 3)/(t-0) = (20-3)/(7-0)
W(t) - 3 = t*17/7
W(t) = (17/7)*t + 3
d)
slope = 17/7 toms/month
daily incraese = 17/210 tons/day