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CAIE pure math P2&3 Logarithmic and Exponential Functions question
- Thread starter Tony2023
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[imath]\rightarrow y = C(a^x)[/imath]
[imath]\rightarrow ln(y) = ln(c) + xln(a)[/imath]
[imath]\rightarrow ln(y) = ln(a)x + ln(c)[/imath]
[imath]\implies gradient = ln(a)[/imath]
[imath]\implies y-intercept = ln(c)[/imath]
[imath]\rarr[/imath] You can now sketch the graph and find what's the gradient and y-intercept.
[imath]rarr[/imath] Then use the above two equations for gradient and y-intercept to find the values of a and c respectively.
[imath]\rightarrow ln(y) = ln(c) + xln(a)[/imath]
[imath]\rightarrow ln(y) = ln(a)x + ln(c)[/imath]
[imath]\implies gradient = ln(a)[/imath]
[imath]\implies y-intercept = ln(c)[/imath]
[imath]\rarr[/imath] You can now sketch the graph and find what's the gradient and y-intercept.
[imath]rarr[/imath] Then use the above two equations for gradient and y-intercept to find the values of a and c respectively.
I have used your idea to done. But I calculate the gradient is 0.39? Is right?
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For that, you will have to sketch the graph and take points at least more than half the graph to find the gradient.
OK, thanks.
