Figuring an amount with a percent in the problem

Question

If you work 15 minutes per day for a week and want to increase your time 40% each week, what week will you be working 40 minutes per day?

Answer 1

Also, if you want to find out how many minutes you will work after x weeks, you can do the calculation 

 

15*1.40^x.

 

This is because the amount of minutes worked after

 

1 week = 15*1.40 = 15*1.40^1

2 weeks = 15*1.40*1.40 = 15*1.40^2

3 weeks = 15*1.40*1.40*1.40 = 15*1.40^3

4 weeks = 15*1.40*1.40*1.40*1.40 = 15*1.40^4

 

...and so on

 

If you want to solve for your problem for any number of weeks, say how many weeks until you have worked t amount of time, then the equation becomes

 

t = 15*1.40^x

 

To solve this for t, first divide both sides by 15:

 

t/15 = 1.40^x

 

Taking the log of both sides:

 

log (t/15) = log (1.40^x)

 

using a log rule

 

log (t/15) = x* log (1.40)

 

divide both sides by log(1.40)

 

log(t/15) / log (1.40) = x = the amount of weeks it will be when you are working t minutes. 

 

Answer 2

Each week you work what you worked the previous week plus 40% (.40) of that time, or 140% (1.40) of what you worked the previous week. Therefore, to get the time worked in a week, you multiply the time worked the previous week by 1.40

1st week: 15 min

2nd week: 15*1.40=21 min

3rd week: 21*1.40=29.4 min

4th week:29.4*1.40=41.16 min - more than 40 minutes

Answer: week 4