Interactive practice questions
In Valera, the average monthly rainfall is recorded.
Plot the average monthly rainfall over a two-year period, letting $x=1$x=1 correspond to January of the first year.
| Month | Rainfall (cm) | Month | Rainfall (cm) |
|---|---|---|---|
| Jan | $1.5$1.5 | July | $11.5$11.5 |
| Feb | $1.5$1.5 | Aug | $12.5$12.5 |
| Mar | $3.5$3.5 | Sept | $11$11 |
| Apr | $7$7 | Oct | $7.5$7.5 |
| May | $9.5$9.5 | Nov | $4.5$4.5 |
| June | $11.5$11.5 | Dec | $2$2 |
The highest average monthly rainfall is $12.5$12.5 cm, and the lowest average monthly rainfall is $1.5$1.5 cm. Their average is $7$7 cm. The line that represents the average annual temperature is graphed below. What is the equation of this line?
The average rainfall can be approximated using a sine wave. Which curve best approximates the average rainfall in Valera? Use your graph from the previous questions to help you.
Use your answer from part (c) to complete the statement:
The sine curve that best approximates the average monthly rainfall has an amplitude of $\editable{}$ cm, a period of $\editable{}$ months, and a phase shift of $\editable{}$ months.
The population (in thousands) of two different types of insects on an island can be modelled by the following functions: Butterflies: $f\left(t\right)=a+b\sin\left(mt\right)$f(t)=a+bsin(mt), Crickets: $g\left(t\right)=c-d\sin\left(kt\right)$g(t)=c−dsin(kt)
$t$t is the number of years from when the populations started being measured, and $a$a,$b$b,$c$c,$d$d,$m$m, and $k$k are positive constants. The graphs of $f$f and $g$g for the first $2$2 years are shown below.
A metronome is a device used to help keep the beat consistent when playing a musical instrument. It swings back and forth between its end points, just like a pendulum.
For a particular speed, the given graph represents the metronome's distance, $x$xcm, from the centre of its swing, $t$t seconds after it starts swinging. Negative values of $x$x represent swinging to the left, and positive values of $x$x represent swinging to the right of the centre.
Sounds around us create pressure waves. Our ears interpret the amplitude and frequency of these waves to make sense of the sounds.
A speaker is set to create a single tone, and the graph below shows how the pressure intensity ($I$I) of the tone, relative to atmospheric pressure, changes over $t$t seconds.