Question

Exit Ticket:

How can we tell from the equation of the
exponential function if it is an exponential
growth or an exponential decay?​

Answer 1

• growth: base is > 1
• decay: base is < 1

Explanation:

If the base of the exponential function is more than 1, then increasing the exponent will increase the value of the function. The value will grow.

If the base of the exponential function is less than 1, then increasing the exponent will decrease the value of the function. The value will decay.

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The above statements assume a positive coefficient of the exponent variable. If the coefficient is negative, the descriptions of growth and decay are reversed.

For example, some exponential functions are written using "e" as a base. The value of e is about 2.71828, so is greater than 1. Such a function will be a growth function if the exponent has a positive coefficient, a decay function otherwise.