What is the formula for converting monthly growth rate to annual growth rate?

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Discussion Overview

The discussion revolves around converting a monthly growth rate to an annual growth rate using the equation Q(t) = 8(0.87)^t, where t represents time. Participants are exploring the initial steps to set up the problem and the relationships between different time units.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant seeks guidance on the first step to find the annual and daily growth rates from the given equation.
  • Another participant questions the units of t, suggesting it may represent years.
  • A different participant clarifies that t represents months in the equation.
  • There is a suggestion to determine how many months are in a year and how many are in a day to substitute those values back into the equation.
  • One participant shares their attempts at calculations, including using 8(0.87)^12 and 8(0.87)^(1/12), and questions whether they are using the correct numbers or setting up the equation correctly.
  • Another participant advises on converting months to years and confirms that the second formula used by the original poster is correct.

Areas of Agreement / Disagreement

Participants generally agree on the need to convert months to years for the calculations, but there remains some uncertainty regarding the correct setup of the equation and the values to use.

Contextual Notes

There are unresolved questions about the correct interpretation of the growth rate and the specific calculations needed to derive annual and daily rates from the monthly growth rate.

vt33
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Hello, my problem is:

Let Q(t) = 8(0.87)^t

Find the annual and daily growth rate.
Can anyone tell me how to set this up? I don't want you to show me the whole problem, just the 1st step. Thanks a ton!
 
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what units does t have? years?
 
units

t=months in the equation
 
Ok so how many t in a year? How many t in a day? Just sub those relationships back into the equation and you got your answers.
 
?

OK, this is what I tried. 8(0.87)^12 and I get 1.50425. I also tried 8(0.87)^(1/12) and I get 7.46. I also tried using 0.13 in replace of 0.87. As you can see, I have tried everything I can think of and tried to manipulate this all I can. Am I using the right numbers? Or, am I setting up the equation incorrectly?
 
Think about how to convert months to years. t months * 1 year/12 months = t years. I hope I didn't lose you when I multiplied by that constant. I'm saying your second formula is right.
 

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