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Last year, the total revenue for Home Style, a national restaurant chain, increased 
5.25% over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let 
m represent months.]
(1) 
(1.0525)^(mt)
(3) 
(1.00427)^(m)
(2) 
(1.0525)^((12 )/(m))
(4) 
(1.00427)^((m)/( 12))

Last year, the total revenue for Home Style, a national restaurant chain, increased 5.25% 5.25 \% over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let m m represent months.]\newline(11) (1.0525)mt (1.0525)^{m t} \newline(33) (1.00427)m (1.00427)^{m} \newline(22) (1.0525)12m (1.0525)^{\frac{12}{m}} \newline(44) (1.00427)m12 (1.00427)^{\frac{m}{12}}

Full solution

Q. Last year, the total revenue for Home Style, a national restaurant chain, increased 5.25% 5.25 \% over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let m m represent months.]\newline(11) (1.0525)mt (1.0525)^{m t} \newline(33) (1.00427)m (1.00427)^{m} \newline(22) (1.0525)12m (1.0525)^{\frac{12}{m}} \newline(44) (1.00427)m12 (1.00427)^{\frac{m}{12}}
  1. Question Prompt: The question_prompt: What expression should the company's chief financial officer use to approximate their monthly percent increase in revenue given a 5.25%5.25\% annual increase?
  2. Convert Annual Rate to Monthly Rate: To find the monthly percent increase, we need to convert the annual increase rate to a monthly rate. Since there are 1212 months in a year, we need to find the 1212th root of the annual increase factor to get the monthly increase factor.
  3. Calculate 1212th Root of Annual Increase Factor: The annual increase factor is 1.05251.0525 (which represents a 5.25%5.25\% increase). To find the monthly increase factor, we calculate the 1212th root of 1.05251.0525.
  4. Express 1212th Root as Monthly Increase Factor: The 1212th root of 1.05251.0525 can be expressed as (1.0525)112(1.0525)^{\frac{1}{12}}. This will give us the factor by which the revenue increases each month.
  5. Find Monthly Increase Factor: Using a calculator or a mathematical software to find the 12th12^{th} root of 1.05251.0525, we get approximately 1.004271.00427. This means that the monthly increase factor is approximately 1.004271.00427.
  6. Final Expression for Monthly Percent Increase: The expression that the company's chief financial officer should use to approximate their monthly percent increase in revenue is therefore (1.00427)m(1.00427)^m, where mm represents the number of months.

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