The diagram shows water in a pool which is in the shape of a triangular prism. The pool is being emptied of water at a constant rate.
Which graph best illustrates the change in depth of water with time?
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The diagram shows water in a pool which is in the shape of a triangular prism. The pool is being emptied of water at a constant rate.
Which graph best illustrates the change in depth of water with time?
\(D\)
\(\text{Eliminate B and C as water depth decreases with time.}\)
\(\text{Eliminate A as rate of flow out of the tank is not linear.}\)
\(\Rightarrow D\)
The diagram shows a container, closed at the base. It is to be filled with water at a constant rate.
Which graph best shows the depth of water in the container as time varies?
`A`
The container will fill at a constant rate for the cylindrical section of the container → a straight line (linear graph).
The container will fill more slowly at a decreasing rate for the conical section of the container → a curved line (non-linear graph).
Therefore, `A` and `B` are the only options.
It cannot be graph `B` as it shows the depth increasing at an increasing rate after the straight line section.
`=>A`
The diagram shows a container which consists of a small cylinder on top of a larger
cylinder.
The container is filled with water at a constant rate to the top of the smaller cylinder. It takes 5 minutes to fill the larger cylinder.
Draw a possible graph of the water level in the container against time. (2 marks)
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Each year the number of fish in a pond is three times that of the year before.
Complete the table above showing the number of fish in 2021 and 2022. (2 marks)
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a.
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Year}\rule[-1ex]{0pt}{0pt} & \ \ \ 2020\ \ \ & \ \ \ 2021\ \ \ & \ \ \ 2022\ \ \ & \ \ \ 2023\ \ \ \\
\hline
\rule{0pt}{2.5ex}\textit{Number of fish}\rule[-1ex]{0pt}{0pt} & 100 & 300 & 900 & 2700\\
\hline
\end{array}
c. The more suitable model is exponential.
A linear dataset would graph a straight line which is not the case here.
An exponential curve can be used to graph populations that grow at an increasing rate, such as this example.
a.
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Year}\rule[-1ex]{0pt}{0pt} & \ \ \ 2020\ \ \ & \ \ \ 2021\ \ \ & \ \ \ 2022\ \ \ & \ \ \ 2023\ \ \ \\
\hline
\rule{0pt}{2.5ex}\textit{Number of fish}\rule[-1ex]{0pt}{0pt} & 100 & 300 & 900 & 2700\\
\hline
\end{array}
b.
c. The more suitable model is exponential.
A linear dataset would graph a straight line which is not the case here.
An exponential curve can be used to graph populations that grow at an increasing rate, such as this example.
Adam travels on a straight road away from his home. His journey is shown in the distance – time graph.
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On the above, complete the distance-time using the information provided. (2 marks)
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`text{Speed: Adam increases speed until approximately}\ \ t=2,`
`text{and then decreases speed until he stops when}\ \ t=4.`
`text{Distance travelled: Adam’s distance from home increases}`
`text{at an increasing rate until}\ \ t=2, \ text{and then continues}`
`text{to increase but at a decreasing rate until}\ \ t=4, \ text(when the)`
`text(distance from home remains the same.)`
a. `text{Speed: Adam increases speed until approximately}\ \ t=2,`
`text{and then decreases speed until he stops when}\ \ t=4.`
`text{Distance travelled: Adam’s distance from home increases}`
`text{at an increasing rate until}\ \ t=2, \ text{and then continues}`
`text{to increase but at a decreasing rate until}\ \ t=4, \ text(when the)`
`text(distance from home remains the same.)`
b. `text(S)text(ince Adam travels home at a constant speed, the graph is)`
`text{is a straight line and ends at (10, 0).}`
Five rabbits were introduced onto a farm at the start of 2018. At the start of 2019 there were 10 rabbits on the farm. It is predicted that the number of rabbits on the farm will continue to double each year.
The container shown is initially full of water.
Water leaks out of the bottom of the container at a constant rate.
Which graph best shows the depth of water in the container as time varies?
A. | B. | ||
C. | D. |
`D`
`text(Depth will decrease slowly at first and accelerate.)`
`=> D`
Water was poured into a container at a constant rate. The graph shows the depth of water in the container as it was being filled.
Which of the following containers could have been used to produce this result?
A. | B. | ||
C. | D. |
`B`
`text(S)text(ince the graph is a straight line, the cup fills up at)`
`text(a constant rate.)`
`=> B`