Answer to Question #48262 in Linear Algebra for Kerri

Question

competitors race distance of 28 m
Competitor 1 ant
Comp 2 snake
Comp 3 frog

use problem-solving strategies find the following information to synthesise mathematical models that represents the following situations. Ensure that each procedure and decision made is justified in a clear, concise and logical manner.

Three mathematical functions, using d for distance as the dependant variable and t for time (in minutes) as the independent variable are to be generated:
• One linear function in the form d=mt

• One quadratic function in the form d=at2 + bt

• One cubic function in the form d = pt3 + qt2 + rt

Each function must describe a competitor’s race performance.
What happens at any point in the race can be predicted mathematically from these functions.
You are to choose values for the constants, m, a,b, p, q & r so following conditions are satisfied:
All take at least 25 mins to finish race but no longer than 35 mins
all start at same time
deadheat between 2 but not 3
during race must be 3 overtakings