Explanation
In general, an exponential equation has the form
[tex]a\cdot b^t=c,[/tex]
where a, b, and c are constants. The percent rate of change of such an equation is given by
[tex]b-1.[/tex]
If this number is positive, we talk about growth; but if this number is negative, we talk about decay.
With this in mind, let's solve the exercise:
• The percent rate of change of the first equation is
[tex]1.6-1=0.6;[/tex]
which in percentage form turns out to be
[tex]0.6\cdot100=60\%.[/tex]
• The percent of change of the second equation is
[tex]1.4-1=0.4;[/tex]
which in percentage form turns out to be
[tex]0.4\cdot100=40\%\text{.}[/tex]
• The percent rate of change of the third equation is
[tex]0.8-1=-0.2.[/tex]
Which in percentage form turns out to be
[tex]-0.2\cdot100=-20\%\text{.}[/tex]
• The percent rate of change of the fourth equation is
[tex]0.2-1=-0.8;[/tex]
which is percentage form is
[tex]-0.8\cdot100=-80\%\text{.}[/tex]
• The percent rate of change of the last equation is
[tex]0.6-1=-0.4;[/tex]
which in percentage form is
[tex]-0.4\cdot100=-40\%\text{.}[/tex]Answer
