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

In summary, the conversation discusses how to find the annual and daily growth rate using the equation Q(t) = 8(0.87)^t. The participants also discuss how to set up the equation and the units of t in the equation. They suggest using the relationship between months and years to find the answers. Various attempts are made to manipulate the equation, and the participant asks for clarification on their approach.
  • #1
vt33
25
0
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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  • #2
what units does t have? years?
 
  • #3
units

t=months in the equation
 
  • #4
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.
 
  • #5
?

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?
 
  • #6
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.
 

What is the difference between annual and daily growth rate?

Annual growth rate refers to the percentage increase in a given quantity over the course of one year, while daily growth rate refers to the percentage increase in a given quantity over the course of one day.

How is annual growth rate calculated?

Annual growth rate can be calculated by dividing the final value of a quantity by the initial value, subtracting 1, and then multiplying by 100 to convert to a percentage.

Why is it important to track annual and daily growth rates?

Tracking growth rates allows scientists to monitor changes in a specific quantity over time and determine if it is increasing, decreasing, or remaining stable. This information can be used to make predictions and inform decision-making.

What factors can influence annual and daily growth rates?

Annual and daily growth rates can be influenced by a variety of factors, such as environmental conditions, availability of resources, genetic factors, and competition with other organisms.

How do annual and daily growth rates impact the environment?

Annual and daily growth rates can have a significant impact on the environment, as they can affect the population sizes and dynamics of different species. They can also influence the productivity and resilience of ecosystems.

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