CAIE pure math P2&3 Logarithmic and Exponential Functions question

[Tony2023]

Hey guys, can you tell me how to calculate the C and a?

 

[Lemniscates]

[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.

 

[Tony2023]

[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.

I have used your idea to done. But I calculate the gradient is 0.39? Is right?

 

[Lemniscates]

I have used your idea to done. But I calculate the gradient is 0.39? Is right?

For that, you will have to sketch the graph and take points at least more than half the graph to find the gradient.

 

[Tony2023]

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.

 

[Ongani]