. A newborn blue whale is approximately 7.2 meters long and weighs 3 tons. When it is weaned at the age of 30weeks it is approximately 16 meters long and weighs 23 tons. LetLbe its length in meters,Mbe its mass in tonsandtbe its age in weeks.(a) Assume thatLandtare linearly related. What is the weekly increase in the length of the calf? Write downan equation forLin terms oft. What is the length of a 12 week old calf
Question
. A newborn blue whale is approximately 7.2 meters long and weighs 3 tons. When it is weaned at the age of 30weeks it is approximately 16 meters long and weighs 23 tons. LetLbe its length in meters,Mbe its mass in tonsandtbe its age in weeks.(a) Assume thatLandtare linearly related. What is the weekly increase in the length of the calf? Write downan equation forLin terms oft. What is the length of a 12 week old calf
Solution
(a) To find the weekly increase in the length of the calf, we need to find the slope of the line that connects the two points given. The slope of a line is given by the change in y divided by the change in x. In this case, y is the length (L) and x is the time (t).
The two points given are (0, 7.2) and (30, 16).
The change in y (ΔL) is 16 - 7.2 = 8.8 meters. The change in x (Δt) is 30 - 0 = 30 weeks.
So, the weekly increase in the length of the calf (slope) is ΔL/Δt = 8.8/30 = 0.293 meters/week.
The equation for L in terms of t is given by the point-slope form of the equation of a line, which is L - L1 = m(t - t1), where m is the slope, and (t1, L1) is a point on the line. Using the point (0, 7.2), the equation becomes L - 7.2 = 0.293(t - 0), or L = 0.293t + 7.2.
To find the length of a 12 week old calf, substitute t = 12 into the equation to get L = 0.293(12) + 7.2 = 10.516 meters.
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