Question

Like other honey bees, giant honey bees use waggle dances to indicate the locations of forage and potential new homes to their nestmates. Mathematically, the direction to a target resource indicated by a waggle phase of a dance is a function of the angle that a bee dances and the distance to the target is a function of the duration of the waggle phase. Analysis of experimental data [1, 2] suggested the following approximate relationship between the observed waggle phase duration of giant honey bees, t (in seconds), and distance indicated by the waggle phase, d(t) (in metres):

d(t)≈{ 180t + 207.4 for 0 < t ≤1.9775

   { 394t - 215.48 for t > 1.9775

The durations of individual waggle phases are often quite variable within a dance. From experimental data for the study in [2], a worker produced a dance with 4 circuits with waggle phase durations: 1.95, 1.79, 2.57 and 2.37 seconds. What distance was indicated by each waggle phase (to the nearest metre)?

1.95 seconds indicated an approximate distance of:    (m)

1.79 seconds indicated an approximate distance of:    (m)

2.57 seconds indicated an approximate distance of: (m)

2.37 seconds indicated an approximate distance of:    (m)

A method for determining a best estimate of the distance described by an entire dance is to calculate the mean distance indicated by all dance circuits. What was the average distance indicated by the 4 dance circuits (to the nearest metre)?

Mean distance =    (m).

Answer 1

The distance as function of time is

1.95 seconds indicated an approximate distance of .

1.79 seconds indicated an approximate distance of

2.57 seconds indicated an approximate distance of

2.37 seconds indicated an approximate distance of

The average distance is