Joe's doctor wants him to exercise

Question

joe's doctor suggests that he start an exercise program. The doctor suggest he begin with exercising 10 minutes daily and increase this amount by 25% oer week until he reaches 30 minutes daily. Using the suggestion of the doctor, how many weeks will it take him to reach his goa

Answer 1

Try using a table to solve the problem. Each time you add a week, add 25% of the number of minutes from the previous week to the number of minutes in the previous week. Keep going until you get to a number bigger than or equal to 30 and see how many weeks it has been.

 

Number of Weeks     | Number of Minutes

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0                             | 10

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1                             | 10 + 0.25*10 = 12.5

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2                             | 12.5+0.25*12.5=15.625

 

You could also solve this problem using a formula. Looking at the table you might notice that we are repeatedly multiplying by 1 + 0.25 = 1.25. This can be modeled using an exponential function f(x) = 10(1.25)^x where x is the number of weeks that have passed and f(x) gives the number of minutes exercised that week. You could find how long it would take to reach 30 minutes of exercise by replacing f(x) in the function with 30 and solving for x.

30 = 10(1.25)^x