Answer:
[tex]f(x)=-\frac{1}{2}(10^x)[/tex]
Step-by-step explanation:
Let the exponential function be [tex]f(x)=a(b^x)[/tex].
When x=0, [tex]f(0)=-\frac{1}{2}[/tex]
[tex]-\frac{1}{2}=a(b^0)[/tex]
[tex]a=-\frac{1}{2}[/tex]
The function now becomes [tex]f(x)=-\frac{1}{2}(b^x)[/tex]
When x=1, f(1)=-5
This implies that:
[tex]-5=-\frac{1}{2}(b^1)\\ \implies b=10[/tex]
Therefore the equation for the exponential function represented in the table below is [tex]f(x)=-\frac{1}{2}(10^x)[/tex]
