Question

Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.5(1/4) x

Answer 1

4x you had  0.5x are the y -intercept.

How can you tell whether an exponential function is growing or deteriorating?

• As the exponential's base is greater than 1, which occurs when those numbers increase, we are seeing exponential growth.
• When the exponential's base is between 1 and 0, and those numbers decrease, we have exponential decay.

You can obviously plot it but if you can also conside that in your function you have 4x

; this tells you that as

x increases (gets bigger) certainly

4x will increase as well (you can consider

4²= 16 and 4³ = 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

4x you had  0.5x .

Learn more about exponential function

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