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

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

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Answer 1 · 2015-09-10T23:51:11

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

Explanation:

For example, if a population is growing at 4% per year, with an initial population of 1000, then $P = f (t) = 1000 \cdot {1.04}^{t}$ $P=f(t)=1000*1.04^t$ is a good model. Note that $\frac{f (t + 1)}{f (t)} = 1.04$ $(f(t+1))/f(t)=1.04$ for all $t$ $t$ , meaning that there is 4% growth over every time interval of length 1.

This can also be written in terms of $e \approx 2.71828$ $e approx 2.71828$ as $P = f (t) = 1000 \cdot e^{k t}$ $P=f(t)=1000*e^(kt)$ . The value of $k$ $k$ is determined by setting $e^{k} = 1.04$ $e^(k)=1.04$ so that $k = ln (1.04) \approx 0.0392$ $k=ln(1.04) approx 0.0392$ .

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

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