SOLUTION: Which function describes exponential decay?
a.f(x)=6(1.01)^x c.f(x)=25(0.8)^x
b.f(x)=3.4(40)^2x d.f(x)=8(17)^a/4
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Question 1090678: Which function describes exponential decay?
a.f(x)=6(1.01)^x c.f(x)=25(0.8)^x
b.f(x)=3.4(40)^2x d.f(x)=8(17)^a/4
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Multiple choice questions often require quick answers.
If you have the time, you can try for visualizing,
and achieving a deeper understanding.
When faced with such a question on a timed test, think smart (and fast).
A function that describes exponential decay
would be one that decreases as increases.
Obviously, with a base greater than ,
and no minus sign before the in the exponent,
the functions
,
, and
increase as increases.
The only plausible answer is
.
Maybe you would recognize as describing exponential decay,
if I wrote it in an equivalent form.
-->-->-->-->--> .
Would you like to see as the base of the exponential function?
-->-->
.
Can you see why decreases?
,
,
, and
.
Can you see why increases?
,
,
, ...
You do not even need to calculate that far.
You must know that ,
,
, and
are all exponential functions,
and you must know that exponential functions are monotonous,
meaning that they either increase all the way from to ,
or decrease all the way from to .
If you find that an exponential function where
(or that for some ), you know that the function increases throughout its domain.
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