An ecologist tracks the migration of a tagged bird
MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
An ecologist tracks the migration of a tagged bird. GPS data give the bird’s speed s(t) (in meters per second) at the times shown.
t (s)
3
8
12
17
21
26
s(t) (m/s)
6.1
7.4
8.0
7.8
7.2
6.5
Because the data logger failed at t=0, no speed was recorded at the start. For the purpose of analysis, assume the bird’s initial speed at t=0 equals the recorded speed at t=3.
(a) Using the assumption above and treating speed as varying linearly between recorded times, approximate the bird’s total flight distance from t=0 to t=26 seconds.
(b) Repeat the approximation in part (a) without making any assumption about the interval 0≤t≤3, that is, by beginning your calculation at t=3 seconds.
(c) Compare the results of parts (a) and (b). Which estimate is more likely to be accurate? Provide a reasoned argument that references features of the data and the modeling assumptions.