Here is a question I want you to look into. I want to see where I have gone wrong.

In 1948 there was 823 cancerpatients. I 1993 there was 5707 cancerpatients. Find the values a and b. Facit: a = 1.045 b = 770

This is what I have done to find these values:

1993-1948= 45 years

823=b*a^0 --> 823/(a^0) = b

5707=b*a^45 --> 5707/(a^45) = b

823/(a^0) = 5707/(a^45) --> (a^45)/(a^0) = 5707/823

a^0 = 1

a = 45sq.root(5707/823) = 1.044

Now I have the value for a. Now for b:

5707/(1.044^45) = 822

eller

823/(1.044^0) = 823

How come b is not the same as the facit? What did I do wrong?