We know that the general form of the exponential equation is [tex] y=a(b)^x [/tex]. We also know that when a>0 and 0<b<1, then this exponential equation will represent an exponential decay.
Now, the expression given to us is [tex] y= 5.8(\frac{3}{7})^x [/tex]
As we can see from this equation, a=5.8>0, and [tex] b=\frac{3}{7} [/tex], thus, 0<b<1, since, [tex] 0<\frac{3}{7}<1 [/tex] and thus, as per the general form, the given equation [tex] y= 5.8(\frac{3}{7})^x [/tex] represents exponential decay.
For a better understanding of the explanation provided here, the graph of [tex] y= 5.8(\frac{3}{7})^x [/tex] has been attached. As can be seen from that graph it indeed is an exponential decay.
