How do you determine if the equation #y = 30(2^x)# represents exponential growth or decay?

Answer 1

You determine whether the equation represents exponential growth or decay by examining the base of the exponent. If the base is greater than 1, such as in the equation y = 30(2^x), it represents exponential growth. If the base is between 0 and 1, exclusive, it represents exponential decay.

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Answer 2

Abigail Allen

The eqn. represents Exponential Growth.

The eqn. represents exponential growth. This is since the Exponential fun. #2^x# is an increasing fun., i.e., to say that as #x# increases, so does #f(x)=2^x# and hence, #y=30*2^x#.

In general, an Exponential Fun. #F(x)=a^x, x in RR# is increasing fun., if #a>1# and is decreasing if # a in (0,1).#

In case, this is helpful, the pleasure all mine! Enjoy Maths.!

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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.