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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?

Respuesta :

YeetyYeetington
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 !!
adioabiola

The value of the expression for case m = -3 is; N = 300.

What does the value represent?

The value of the expression for m= -3 can be evaluated as follows;

N = 8100 × 3^(-3)

N = 8100 × (1/27

N = 300.

On this note, the value represent the number of visitors 3 months before the number of visitors was measured.

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