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S=140(0.995)^(m)
The given equation models the number of subscribers in thousands, 
S, of a newspaper 
m months after 2008. Which of the following equations models the number of subscribers, in thousands, of the newspaper 
y years after 2008 ?
Choose 1 answer:
(A) 
S=140(0.942)^((y)/( 12))
(B) 
S=140(0.942)^(12 y)
(c) 
S=140(0.995)^((y)/( 12))
(D) 
S=140(0.995)^(12 y)

S=140(0.995)m S=140(0.995)^{m} \newlineThe given equation models the number of subscribers in thousands, S S , of a newspaper m m months after 20082008. Which of the following equations models the number of subscribers, in thousands, of the newspaper y y years after 20082008 ?\newlineChoose 11 answer:\newline(A) S=140(0.942)y12 S=140(0.942)^{\frac{y}{12}} \newline(B) S=140(0.942)12y S=140(0.942)^{12 y} \newline(C) S=140(0.995)y12 S=140(0.995)^{\frac{y}{12}} \newline(D) S=140(0.995)12y S=140(0.995)^{12 y}

Full solution

Q. S=140(0.995)m S=140(0.995)^{m} \newlineThe given equation models the number of subscribers in thousands, S S , of a newspaper m m months after 20082008. Which of the following equations models the number of subscribers, in thousands, of the newspaper y y years after 20082008 ?\newlineChoose 11 answer:\newline(A) S=140(0.942)y12 S=140(0.942)^{\frac{y}{12}} \newline(B) S=140(0.942)12y S=140(0.942)^{12 y} \newline(C) S=140(0.995)y12 S=140(0.995)^{\frac{y}{12}} \newline(D) S=140(0.995)12y S=140(0.995)^{12 y}
  1. Given Equation Transformation: We are given the equation S=140(0.995)mS = 140(0.995)^m, where SS is the number of subscribers in thousands and mm is the number of months after 20082008. We need to convert this equation to reflect the number of subscribers yy years after 20082008. Since there are 1212 months in a year, we can express mm in terms of yy by the relation m=12ym = 12y.
  2. Substitution and Simplification: Substitute m=12ym = 12y into the original equation to get the equation in terms of yy years.S=140(0.995)12yS = 140(0.995)^{12y}
  3. Option Analysis: Now we need to check the given options to see which one matches the equation we derived. Option (A) has a different base for the exponent, option (C) has the wrong exponent, and option (D) is the correct form of the equation we derived. Option (B) has the exponent 12y12y but with the wrong base.
  4. Final Equation: Therefore, the correct equation that models the number of subscribers in thousands of the newspaper yy years after 20082008 is:\newlineS=140(0.995)(12y)S = 140(0.995)^{(12y)}

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