How do you determine if the equation #y = 2.1(0.15)^x# represents exponential growth or decay?

Answer 1

To determine if the equation ( y = 2.1(0.15)^x ) represents exponential growth or decay, examine the base of the exponential function. If the base is greater than 1, it represents exponential growth. If the base is between 0 and 1, exclusive, it represents exponential decay. In this case, the base ( 0.15 ) is between 0 and 1, so the equation represents exponential decay.

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Answer 2

Nathan Axel

y decays as x increases..

Let #y=b a^x=be^(x ln a)#

#y'=b ln a e^(x ln a)#

As x increases,,y is decreasing or increasing according as y' > or < 0.

For decay, y' < 0, when b > 0 and 0 < ln a < 1.#

Here, # b=2.1 > 0 and ln a = ln 0.15 = -0.1897 < 0#

So, y decays as x increases.

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Answer from HIX Tutor

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.