Answer::
[tex]y=5(0.5)^x[/tex]
Explanation:
An exponential equation is an equation of the form:
[tex]y=ab^x[/tex]
When x=0, y=5
[tex]\begin{gathered} y=ab^x \\ 5=ab^0 \\ a\times1=5 \\ \implies a=5 \end{gathered}[/tex]
When x=1, y=2.5
[tex]\begin{gathered} y=ab^x \\ 2.5=5\times b^1 \\ b=\frac{2.5}{5} \\ b=0.5 \end{gathered}[/tex]
Therefore, the exponential function represented by the table is:
[tex]y=5(0.5)^x[/tex]
