Alguem sabe como encontro esta funcao?

Question

Em Maio de 2003, uma compania de gas tinha o seguinte plano de cobranca para o uso de gas natural em casas de uma familia unica:
Taxa de servico mensal ->$11.25
Taxa de servico por unidade -> $0.09284/unidade (primeiros 50 unidade)
-> $0.06775/unidade (Mais de 50 unidade)
Cobranca do gas ->$0.1006/unidade
?->Construa a funcao que relaciona o custo mensal C pelos x unidades de gas.
The answers is C(x)=12.50+0.16835x
I can't understand where comes that 12.50. (My answer was 11.25+0.16835x)

Answer 1

Thanks for your effort on translating your problem into Portuguese.

There is not an unique function which describes the cost fee. In fact, there are two cost functions, one for gas usage below 50 therms, and another for gas usage over 50 therms.

Let 'x' be the amount of gas consumed, and let C be the cost function. When 'x' is below 50 therms, C =

11.25+ <--- monthly service fee
+ .1006 times 'x' <--- gas fee no matter what is the gas usage
+ .09284 times 'x' <--- service tax for the first 50 therms of gas
= 11.25+ .19344x

When x is over 50 therms, C =

11.25+ <--- monthly service charge
+ .1006 times x <--- no matter how much gas
+ .09284 times 50 <--- first 50 therms of gas
+ .06775 times (x- 50) <--- remaining amount of gas
= 12.50(45)+ .16835x

The latter function is probably the answer you are looking for.