How do you determine if the equation #y = 0.5(4)^x# represents exponential growth or decay?

Answer 1

To determine if the equation (y = 0.5 \times 4^x) represents exponential growth or decay, you examine the base of the exponential term.

If the base is greater than 1 (in this case, 4), the equation represents exponential growth. If the base is between 0 and 1, exclusive (e.g., 0.5), the equation represents exponential decay.

Since the base in (y = 0.5 \times 4^x) is 4, which is greater than 1, the equation represents exponential growth.

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Answer 2

Ethan Adkins

I would say an exponential growth.

You can obviously plot it but if you can also conside that in your function you have #4^x#; this tells you that as #x# increases (gets bigger) certainly #4^x# will increase as well (you can consider #4^2=16# and #4^3=64#). It is true that you have to multiply by #0.5# but nevertheless the entire function will grow anyway!

Graphically: graph{0.5*(4^x) [-14.24, 14.24, -7.12, 7.12]}

If you want, try to think at the case where instead of having #4^x# you had #0.5^x#...

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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.