- #1

opus

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## Main Question or Discussion Point

Say I have a function that represents the population growth of a certain country that can be written as ##f\left(x\right)=1.25\left(1.012\right)^t##, where t is in years. I can graph this function and it will look a certain way exponentially.

I've looked at a ton of examples, and they're all modeled in years. One thing that I tried is to graph the function ##f\left(x\right)=1.25\left(1.012\right)^{t/12}## to model the graph in months rather than years. I did get a different graph which doesn't increase nearly as fast as the original. Why would the t in years appear to grow faster than t in months? In this population model, wouldn't the growth be consistent throughout the whole year?

What I don't understand here (assuming this is how you would graph the function in terms of months), is when we have an exponential function to the power of t, is it always in years? If we want to model a time frame in anything other than years, do we need to manipulate t to reflect this? Or would we just say t is in months, not years, from the start?

I've looked at a ton of examples, and they're all modeled in years. One thing that I tried is to graph the function ##f\left(x\right)=1.25\left(1.012\right)^{t/12}## to model the graph in months rather than years. I did get a different graph which doesn't increase nearly as fast as the original. Why would the t in years appear to grow faster than t in months? In this population model, wouldn't the growth be consistent throughout the whole year?

What I don't understand here (assuming this is how you would graph the function in terms of months), is when we have an exponential function to the power of t, is it always in years? If we want to model a time frame in anything other than years, do we need to manipulate t to reflect this? Or would we just say t is in months, not years, from the start?