Answer:
a) Figure attached
b) ![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D) 
  
For our case we have this:
n=10  
  
![r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B10%28330.0321%29-%2875.81948%29%2843.5231%29%7D%7B%5Csqrt%7B%5B10%28574.8598%29%20-%2875.819%29%5E2%5D%5B10%28192.8274%29%20-%2843.5231%29%5E2%5D%7D%7D%3D0.989) 
  
So then the correlation coefficient would be r =0.989
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
Solution to the problem 
Part a
Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985
Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7
After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.
Part b
And in order to calculate the correlation coefficient we can use this formula:  
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D) 
  
For our case we have this:
n=10  
  
![r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B10%28330.0321%29-%2875.81948%29%2843.5231%29%7D%7B%5Csqrt%7B%5B10%28574.8598%29%20-%2875.81948%29%5E2%5D%5B10%28192.8274%29%20-%2843.5231%29%5E2%5D%7D%7D%3D0.989) 
  
So then the correlation coefficient would be r =0.989