Given:
The exponential equations in the options.
To find:
The equation which represents exponential decay.
Solution:
The general exponential equation is
[tex]y=ab^x[/tex]
where, a is initial value and b is growth rate.
If b<1, then it is an equation of exponential decay.
If b>1, then it is an equation of exponential growth.
In option A, b=31>1, i.e., exponential growth.
In option B, b=3.1>1, i.e., exponential growth.
In option C, b=0.13<1, i.e., exponential decay.
In option D, b=1.03>1, i.e., exponential growth.
Only [tex]y=10(0.13)^x[/tex] represents exponential decay.
Therefore, the correct option is C.
