The function that models the independent variable, x, in terms of y, is:
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
How to write the independent variable in terms of y?
Here we have the relation:
[tex]y = 2.56*(1.04)^x[/tex]
We want to write x in terms of y, so we just need to isolate x.
We have:
[tex]\frac{y}{2.56} = (1.04)^x[/tex]
Now we can apply the natural logarithm in both sides, so we get:
[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]
Now we can just isolate x.
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
That is the function that models the independent variable, x, in terms of y.
If you want to learn more about natural logarithms:
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