Help with algebra 2 review my retake is tomorrow.

Question

21) 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.] (3) (1.00427)m (4) m (1.00427)12

 

(Can somone explain question 21 on the algebra 2 common core June 2016 regents.)

Answer 1

The problems asks if the CFO knows that the revenue grows by 5.25% a year, how much does the revenue grow every month. In other words by what percent would the restaurant's revenue have to grow every month for the restaurant to gain 5.25% from the original amount.

 

Annual increase based on annual rate = Annual increase based on monthly rate 12 times.

 

The increase in the original amount can be found from the formula: A_o(1 + i)ⁿ, where n = number of time periods and i = interest rate.

 

Therefore,

 

A_o(1 + i_a) = A_o(1 + i_m)^m, where A_o= original amount, i_a = annual interest rate, i_m = monthly interest rate, m = number of months in time period.

 

-> (1 + i_a) = (1 + i_m)^m

 

-> (1 + i_a)^(1/m) = 1 + i_m

 

-> i_m = (1 + i_a)^(1/m)= (1 + 0.525)^(1/12)-1 = 0.04273.

 

Thus, the monthly revenue increase of the restaurant is 0.4273%.

Answer 2

If the increase for the entire year = 5.25%,  then the increase per month is 

found by:  yearly increase / 12 months in a year

 

                          5.25% / 12 = .4375%  (monthly increase)

 

To find the monthly increase in revenue:

 

Revenue for any month = Original Revenue ( 1 + .004375) ^m

 

This equation will get you the amount of revenue for any given month = m

 

Some of your numbers, I don't know what they go to?