Math Problem Statement
A river level rises rapidly during a flood which started at noon on Monday 5 March. The initial depth of the river was 2.3 m. The maximum depth of the river was 4 m, which occurred at noon, 1 day later. By day 3, the depth had dropped to 3 m. The graph of the depth of the river is shown. Part of this graph is to be modelled by a hyperbola of the form d
a t − b + c d= t−b a +c where d d is the depth in metres and t t is the time in days since the rain started.
a. Write down the equation of the hyperbola which could be used to model the depth of the river after it had been raining for 3 days. Round a and b to the nearest integer
Solution
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Math Problem Analysis
Mathematical Concepts
Hyperbola
Equations
Graphing
Formulas
Hyperbola equation d = a / (t - b) + c
Theorems
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Suitable Grade Level
Grades 11-12