# How do you know When to use an exponential growth model?

When the growth is at an approximately constant percent per unit time, an exponential model works well.

This means that a 4% growth rate per unit time corresponds to approximately 3.92% instantaneous growth rate. This basically means that the tangent line at any point grows by approximately 3.92% over a time interval of length 1.

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You should use an exponential growth model when the rate of growth of a quantity is proportional to its current value, meaning the larger the quantity, the faster it grows. This pattern is characteristic of many natural phenomena such as population growth, compound interest, and the spread of diseases in the early stages. Additionally, exponential growth models are appropriate when there are no limiting factors that would cause the growth rate to slow down over time.

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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 arc length of the curve # y = (3/2)x^(2/3)# from [1,8]?
- What is the arclength of #f(x)=e^(x^2-x) # in the interval #[0,15]#?
- What is the general solution of the differential equation? # cosy(ln(secx+tanx))dx=cosx(ln(secy+tany))dy #
- What is a particular solution to the differential equation #dy/dx=cosxe^(y+sinx)# with #y(0)=0#?
- How do you find the arc length of the curve #y=2sinx# over the interval [0,2pi]?

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