Logarithmic Regression Question (TI-84 Plus Graphing Calculator)

[MeesaWorldWide]

TL;DR Summary: Exponential VS Logarithmic Regression (using the TI-84 Plus graphing calculator)

Here is the question:
A scientist examines the growth of bean plants under different growing conditions. The results of one trial are as follows:
Day: 1 3 5 9 11 15
Average height of bean plants (cm) 3.2 4.6 5.4 4.2 5.5 7.1

Determine a logarithmic equation that best represents the data.

I have entered this data into my calculator lists and used logarithmic regression (LnReg) to obtain the equation y = 3.22 + 1.07Lnx
However, the actual answer supposedly requires me to switch the x and y values (inverse), and then use LnReg on that, which produces a different equation: y = -17.30 + 15.60Lnx

I don't understand why I need to switch the x and y values if the data points already trend in a logarithmic fashion. The fact that I was able to use LnReg on the data to get an equation without switching the values should be enough, no? Why is is better to switch x and y first? Why can I not just use the first equation I found (which didn't involve switching anything)?

Thanks in advance for any clarity you can provide.

 

[renormalize]

Thanks in advance for any clarity you can provide.

Your data is "Day" and "Height" but your equations are in terms of variables $x$ and $y$ which you never define!

 

[MeesaWorldWide]

Sorry, should have clarified. If you are familiar with doing regression on a TI-84 calculator, there are two lists (L1 and L2) that the data gets entered into. I entered my time (Days) into L1 (x-axis) and my heights into L2 (y-axis). I am unsure why they need to be switched to get the best answer since I already get a logarithmic equation when Days is the independent variable and height is the dependent variable. My second equation that I stated is the supposed 'best' answer, but it has Days on the y axis and the height is the independent variable (?) which doesn't really make sense by itself.
Note that the question itself never defines for me which variables is x and which is y. The questions is written exactly as I typed it out here.

 

[renormalize]

I am unsure why they need to be switched to get the best answer since I already get a logarithmic equation when Days is the independent variable and height is the dependent variable. My second equation that I stated is the supposed 'best' answer, but it has Days on the y axis and the height is the independent variable (?) which doesn't really make sense by itself.

Sorry, I am not familiar with the operation of the TI-84+ calculator. Can it quantify "the goodness of fit" by displaying, e.g., the Coefficient of Determination $R^2$ for each of the two logarithmic fits? If so, which fit has the higher value?

 

[FactChecker]

Their answer is bad for the reason that the errors that are sum-square minimized by the regression are the wrong errors.