The amount of water, A, in thousands of litres, available in a water tank located on a farm fluctuates in a yearly cycle and can be modelled by the function A(t) = a sin (kt) +b, where t is the elapsed time, in weeks, since the start of the year. The amount of water available in the tank on week 6 is 24 thousand litres and on week 31 is 9.2 thousand litres. (a) Find the value of k, in degrees, assuming there are 52 whole weeks in a year. (b) Set up a pair of equations to find the value of a and the value of b. Give your answers correct to the nearest integer. (c) Hence find the amount of water available in the tank in week 42. A(t) on the grid below, for one full year, indicating clearly (d) Draw the graph of the minimum and maximum points.
The amount of water, A, in thousands of litres, available in a water tank located on a farm fluctuates in a yearly cycle and can be modelled by the function A(t) = a sin (kt) +b, where t is the elapsed time, in weeks, since the start of the year. The amount of water available in the tank on week 6 is 24 thousand litres and on week 31 is 9.2 thousand litres. (a) Find the value of k, in degrees, assuming there are 52 whole weeks in a year. (b) Set up a pair of equations to find the value of a and the value of b. Give your answers correct to the nearest integer. (c) Hence find the amount of water available in the tank in week 42. A(t) on the grid below, for one full year, indicating clearly (d) Draw the graph of the minimum and maximum points.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 57E
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