K and N are constant.
K = is the gradient
As we want to calculate the logs of R and T, we must apply to the laws of log rule number 1 which can be potted as log xy=log x +log y.
After separating the logs we must use the log rule number 3, which is
Log x+ k log x.
Keep in mind that the transposition should end up to the linear function Y=c + mx.
- Log k as C, which is the intercept of the line
- N as the gradient of the line and an exponent in the formula
- Log R as the as the base of the exponent n
Log T = log K + n log R is the same as Y = c + mx
I’ve calculated the log of R and T in the below Table for each planet, so I used my calculator and to find log R I typed log58 and I got 1.769427994 and we do same thing for T.
After calculating the all of the logs I have insert them into excel spreadsheet and displayed the equation of the line.
Now that you have the equation y = 1.5001x – 0.7003
I will transfer it to T = KR^n
1.5001 is the gradient, which is n
-0.7003 is the y intercept (c), which is log K but you should transfer Log K to K which is again 10^-0.7003.
Full equation is T = 10^-0.7003 x ( R )^1.5001
Percentage error:
((Actual data -Model) /Actual Data)*100
((88-88.10860661)/88)*100
Conclusion:
After doing the above course work I have found out that, I have achieved many things and I can list them as:
- Calculating the logs of R and T
- Drawing graph by using the result from R and T logs
- Determining an accurate linear equation of logs (both R and T)
- Rearranging log k= 0.7003 into 10^-0.7003 then putting it into the equation of T= kR so it will look like: T= 10^-0.7003* (R) ^1.5001.
- Applying the rules 1 and 3 to rearrange the equation T= KR
- Determining the correct equation for the line T= 10^-0.7003*(R ^1.5001)
