We are asked to determine which functions represent decay. A function represents a decay if the values of "y" decrease as the values of "x" increase. In more general terms, a function represents decay when the values of the dependent variables decrease as the values of the independent variable increase.
In the case of functions of the form:
[tex]y=a(b)^x[/tex]
If we have:
[tex]b<1[/tex]
Then this function represents decay.
In the case of the function:
[tex]y=20\mleft(1-0.23\mright)^x[/tex]
We have:
[tex]b=1-0.23=0.77<1[/tex]
Therefore, this function represents decay
For the function:
[tex]y=\mleft(2/3\mright)^x[/tex]
We have:
[tex]b=\frac{2}{3}<1[/tex]
Therefore, this function represents decay.
In the case of the table we notice that the values of "y" increase as the values of "x" increase, therefore, this does not decay.
