A straight line is fit to a data set $(ln x, y)$. This line intercepts the abscissa at $ln x = 0.1$ and has a slope of $−0.02$. What is the value of $y$ at $x = 5$ from the fit?
I can not understand what is asking in this problem .
Can anyone please help me to understand?
y and lnx have a linear relationship.
Let lnx=t then y=y(t).Therefore y=mt+c———>1
Given that the line has an x intercept at lnx=0.1(y=0).
Using 1, $$0=m(0.1)+c$$ Implies, $$c=-0.1m——->2$$.
Given that the slope is -0.02 which means that m=-0.02.
From 2, $$c=-0.1(-0.02)$$ $$c=0.002$$
Therefore the line equation has to be
$$y=-0.02t+0.002$$ i.e,
$$y=-0.02lnx+0.002$$
Therefore when x=5
$$y=-0.02ln5+0.002$$