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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