Consider the following graphs:
Graph A:
Graph C:
Graph B:
Graph D:
Which graph shows a relationship that is:
Increasing, at an increasing rate?
Decreasing, at a decreasing rate?
Decreasing, at an increasing rate?
Increasing, at a decreasing rate?
Consider the following graphs:
Graph 1:
Graph 2:
Which graph shows a relationship that is:
Decreasing, at a constant rate?
Increasing, at a constant rate?
Describe the rate of change for each of the following graphs:
Consider the function y = 2^{x}. Describe the rate of change of the function.
Consider the function y = \left(\dfrac{1}{3} \right)^{x}. Describe the rate of change of the function.
Consider the function y = \sqrt{x}. Describe the rate of change of the function.
Consider the function y = -\sqrt{x}. Describe the rate of change of the function.
Consider the function y = -5x + 22. Describe the function as increasing or decreasing and comment on its rate of change.
Consider the function y = 7x - 5. Describe the function as increasing or decreasing and comment on its rate of change.
Anna went for a run. She started by gradually increased her speed until she felt comfortable, then kept her speed constant for a little while. She then slowed down as she got tired towards the end of her run.
Which graph shows the total distance covered by Anna, plotted against time?
Graph A:
Graph C:
Graph B:
Graph D:
Graph E:
Graph F:
45 rabbits are released into the wild. In the absence of predators, the population P is expected to grow according to the function P = 36 x^{2} + 9 x + 45, where x is the number of years since release.
Find the expected rabbit population after the following number of years:
| \text{Number of years, }x | 1 | 5 | 10 |
|---|---|---|---|
| \text{Population, }P |
The given graph shows the population over the first 6 years. Describe the rate of change of the rabbit population.
Ned has two graphs. Each graph shows how the height of the water in a vase changes as a constant flow of water is poured in.
Vase A:
Vase B:
Which shape could have produced the graph for Vase A?
Which shape could have produced the graph for Vase B?
An initial chemical reaction results in a chain of chemical reactions that follow:
The total number of reactions after t seconds is given by the equation y = 3^{t}.
How many chemical reactions have occurred by the end of the 3rd second?
How many chemical reactions occur in the 4th second only?
How many chemical reactions occur in the 5th second only?
Describe the rate of increase of the number of reactions.
1 gram of sugar is poured into a cup of water and immediately begins to dissolve. Each second the amount of sugar remaining is \dfrac{1}{4} of the amount present in the previous second.
Complete the table:
| \text{Seconds passed, }t | 1 | 2 | 3 |
|---|---|---|---|
| \text{Undissolved sugar in grams, }y |
Find the difference in undissolved sugar between the first and second seconds.
Find the difference in undissolved sugar between the second and third seconds.
Describe the change in the amount of undissolved sugar over time.