# How long can exponential growth last?

It is infinite.

However, in real life as a model, it works well at the start but runs into problems because resources are always a limiting factor to prevent things to continually grow at an exponential rate. There are many limiting resources such as water, air, energy, food, waste removal, etc.

To more accurately model with resources in mind, see the logistic growth function .

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The duration of exponential growth depends on various factors such as the initial conditions, the rate of growth, and any limiting factors present in the system. In theory, exponential growth can continue indefinitely given ideal conditions, but in reality, it is often limited by factors such as resource availability, competition, or environmental constraints.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the point c in the interval #1<=x<=4# such that f(c) is equation to the average value of #f(x)=abs(x-3)#?
- How do you find the average value of #f(x)=-x^5+4x^3-5x-3# as x varies between #[-2,0]#?
- How to you find the general solution of #(dr)/(ds)=0.05s#?
- Consider the function #f(x) = (x)/(x+2)# on the interval [1, 4], how do you find the average or mean slope of the function on this interval?
- What is a solution to the differential equation #xy' + 2y = 0#?

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