Question

The number of visitors to a certain Web site triples every month. The number of visitors is modeled by the expression 8100 times •3m​, where m is the number of months after the number of visitors was measured. Evaluate the expression for m=−33. What does the value of the expression represent in the​ situation?

Answer 1

Suppose we have had S visitors in n months since EIS (Entry Into Service) of the site, then : 
S(n) = 8100 + 8100 * 3 + 8100 * 3^2 + 8100 * 3^3 + ... +8100 * 3^n 
S(n) = 8100 * [ 1 + 3 + 3^2 + 3^3 + ... + 3^n ] 
and we know that : 
1 + 3 + 3^2 + 3^3 + ... + 3^n = (3^(n+1) - 1)/(3 - 1) 
= (3^(n+1) - 1)/2 
therefore 
S(n) = 8100 * (3^(n+1) - 1)/2 
finally : 
S(n) = 4050 * (3^(n+1) - 1) 
and this allows you to obtain the month n, if you know S(n) : 
3^(n+1) = S(n) /4050 + 1 
therefore : 

n = ln[S(n) /4050 + 1] /ln3 - 1 

hope it' ll help !!