Write down the value of:
33
4-2
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Write down the value of:
33
4-2
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Sketch the graph with equation , stating the coordinates of the point where the graph intersects the -axis and the equation of any asymptotes.
Also state whether this equation would represent exponential growth or decay.
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The following equations can be used for exponential models.
State whether each one would represent exponential growth or exponential decay.
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Write down the value of in the following statements:
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Write down the value of in the following statements:
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Solve the equation
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Solve the equation .
Hence, or otherwise, solve the equation .
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Solve the equation
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Sketch the graph of , clearly showing the coordinates of the point where the graph intercepts the -axis and stating the equations of any asymptotes.
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Given :
Write down an expression for .
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Use a calculator to find the value of
giving your answers to four significant figures.
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Solve the equation , giving your answer in the form where is an integer.
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On the same axes, sketch the graphs of and , labelling any points where the graphs cross the coordinate axes and writing down the equation of any asymptotes.
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Sketch the graph of , stating whether this graph indicates exponential growth or exponential decay.
Find the exact value of when .
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Write down the value of in the following statements.
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Using a calculator, find to 3 significant figures
Solve .
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Solve .
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On the same axes, sketch the graphs of and .
Label any points where the graphs intersect the coordinate axes.
Write down the equations of any asymptotes.
Write down the gradient of at the point .
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Given write down an expression for .
Given write down an expression for .
Find the gradient of at the point where .
Give your answer in the form , where and are integers to be found.
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The function is defined by for
Find .
Describe the transformation from to .
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Solve , giving your answers to 3 significant figures.
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On the same axes, sketch the graphs of and .
Label any points of intersection with the coordinate axes.
Write down the equations of any asymptotes.
Write down an equation for the graph that is a reflection of in the -axis.
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Sketch the graph of .
Find the value of when .
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Find the value of
Write down the value of in the statement .
Evaluate .
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Solve .
Solve .
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Solve .
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Sketch the graph of for .
Label any points of intersection with the coordinate axes.
Write down the equations of any asymptotes.
Write down the gradient of at the point where .
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The function is defined by for .
Find .
Find .
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Solve , giving your answer to 3 significant figures.
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Find the gradient of the curve where and and are constants.
At the point the gradient is 12, find in terms of .
Hence write down y in terms of (and ) only.
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Show that the equation has only one real solution.
Explain why the equation has no real solutions.
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On the same axes, sketch the graphs of and .
Label any points of intersection with the coordinate axes.
Write down the equations of any asymptotes.
Write down an equation for the graph that is a reflection of in the -axis.
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Sketch the graph of , stating whether this graph indicates exponential growth or exponential decay.
Find the value of when .
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Without using a calculator, evaluate .
Show each stage of your solution carefully.
Evaluate .
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Solve .
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Find two values of for which is true.
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Sketch the graph of for .
Label any points of intersection with the coordinate axes.
Write down the equations of any asymptotes.
Find the gradient of at the point where , giving your answer correct to 3 significant figures.
The population growth of population, P, at time, t years, is modelled by the equation
Write down the initial population.
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The function is defined by for .
Find .
Find .
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Find the gradient of the curve where and are constants.
State a condition on to ensure represents exponential decay.
At the point the gradient is 10. Find in terms of (and ) only.
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A particle is travelling with velocity, ms-1, at time seconds.
The velocity of the particle is modelled , where is a constant.
Write down the initial velocity of the particle.
Find an expression (in terms of and ) for the acceleration of the particle.
After 12 seconds the velocity of the particle is 0.9 ms-1.
Find the value of , giving your answer to 3 significant figures.
State a problem with the model for large values of
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Solve .
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Solve the equation , giving answers to 3 significant figures where appropriate.
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