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

Algebra ->  Exponents -> 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       Log On


   

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) About Me  (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 x increases.
Obviously, with a base greater than 1 ,
and no minus sign before the x in the exponent,
the functions
f%28x%29=6%2A1.01%5Ex ,
f%28x%29=3.4%2A4%5E%282x%29 , and
f%28x%29=8%2A17%5E%22x+%2F+4%22 increase as x increases.
The only plausible answer is
highlight%28f%28x%29=25%2A0.8%5Ex%29 .

Maybe you would recognize f%28x%29=25%2A0.8%5Ex as describing exponential decay,
if I wrote it in an equivalent form.
f%28x%29=25%2A0.8%5Ex-->f%28x%29=25%2A%288%2F10%29%5Ex-->f%28x%29=25%2A%288%5Ex%2F10%5Ex%29-->f%28x%29=25%2A%2810%5E%28-x%29%2F8%5E%28-x%29%29-->f%28x%29=25%2A%2810%2F8%29%5E%28-x%29-->f%28x%29=25%2A1.25%5E%28-x%29 .
Would you like to see e as the base of the exponential function?
f%28x%29=25%2A0.8%5Ex-->f%28x%29=25%2A%28e%5Eln%280.8%29%29%5Ex-->f%28x%29=25%2Ae%5E%28ln%280.8%29%2Ax%29
ln%280.8%29=approximately-0.233%29 .

Can you see why f%28x%29=25%2A0.8%5Ex decreases?
0.8%5E0=1 ,
0.8%5E1=0.8 ,
0.8%5E1=0.64 , and
0.8%5E1=0.0512 .
Can you see why f%28x%29=6%2A1.01%5Ex increases?
1.01%5E0=1 ,
1.01%5E0=1.01 ,
1.01%5E0=1.0201 , ...
You do not even need to calculate that far.
You must know that f%28x%29=25%2A0.8%5Ex ,
f%28x%29=6%2A1.01%5Ex ,
f%28x%29=3.4%2A4%5E%282x%29 , and
f%28x%29=8%2A17%5E%22x+%2F+4%22 are all exponential functions,
and you must know that exponential functions are monotonous,
meaning that they either increase all the way from -infinity to infinity ,
or decrease all the way from -infinity to infinity .
If you find that an exponential function where f%281%29%3Ef%280%29
(or that f%28c%29%3Ef%280%29 for some c%3E0 ), you know that the function increases throughout its domain.