02.43findingeqns

Finding Equations for Exponential and Logarithmic Graphs

Given an exponential or logarithmic graph, it is possible to find an equation using any base.

Therefore questions will tend to specify the form of the equation to be found (including the base).

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Example 1 <exponential graph>

… … The rule for the function of the graph shown here
… … is of the form: $y = Ae^x + c$.
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… … Find the values of A and c
… … … (as exact values and correct to 2 decimal places) . .

Example 2 <logarithmic graph>

… … The rule for the function of the graph shown here:
… … is of the form: $y = A\log_e(x + b)$

… … Find the values of A and b
… … … (as exact values and correct to 2 decimal places). . .

Example 3 <exponential graph>

… … Find the equation in the form $y = Ae^bt$,

… … given that y = 6 when t = 1,
… … and y = 8 when t = 2.

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Example 4 <using the Classpad>

… … Using your CAS calculator to find the equation of an exponential graph (base e)
… … that passes through $(1, \; 5) \text{ and } (3, \; 30)$.

… … State the coefficients correct to 3 decimal places

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