How do you Find the exponential growth rate for a given data set?
The quick answer is: Take logs and find the slope.
If your data is exponential, then the log of the data will be linear.
For example, consider the data:
Taking natural logs we find:
If the data set is inexact (e.g. measurements from an experiment), then take logs before performing a linear regression or similar.
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To find the exponential growth rate for a given data set, you can follow these steps:

Determine if the data exhibits exponential growth. This is typically indicated by the data points increasing at a faster rate over time.

Plot the data on a graph, with time on the xaxis and the corresponding values on the yaxis.

Fit an exponential function to the data. This is usually done by using regression analysis or curve fitting techniques. The general form of an exponential function is (y = ab^x), where (a) is the initial value, (b) is the base of the exponential function (growth rate), and (x) is the time.

Once you have the equation for the exponential function, determine the value of (b), which represents the exponential growth rate. This value indicates how much the quantity is growing or decaying over each unit of time.

Interpret the value of (b) as the growth rate. If (b > 1), it indicates exponential growth, while if (0 < b < 1), it indicates exponential decay.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
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