Find the annual percent increase or decrease that y=0.35(2.3)^x models.
if possible, show work.

Question

Find the annual percent increase or decrease that  y=0.35(2.3)^x models.
if possible, show work.

anonymous · Answer

Where x is time in years?

anonymous · Answer

yes.

anonymous · Answer

Well. If you have an exponential function like:
$$y = a(b)^x$$
a will be your starting value, and every time x increases by one, y will be multiplied by the amount b. So here's a simple example of that:
$$y=10(2)^x$$
When x=0, y = 10. 10 is the starting value. Every time x goes up by one, y will be multiplied by 2, or doubled. So
x=1 gives y = 20
x=2 gives y =40
x=3 gives y =80
x=4 gives y = 160
x=5 gives y = 320

Seeing the pattern? So that means that, for this function, y will always be twice as large as last years y. As a percent, that would be 200%

Try to figure out what that means for your problem, and ask me any question you have.

dumbcow · Answer

agree with above ^^
Note: it asks for percent increase/decrease though so you need to subtract 100% essentially
think of it as y = (1+p)^x  where p is rate of increase

anonymous · Answer

Thanks!

anonymous · Answer

Oh right right. My example isn't a 200% increase. It's a 100% increase. Good catch, buddy.