Question

State whether the equation represents exponential growth, exponential decay, or neither : y= 5.8(3/7)^x

Answer 1

We know that the general form of the exponential equation is $y=a(b)^x$. 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 $y= 5.8(\frac{3}{7})^x$

As we can see from this equation, a=5.8>0, and $b=\frac{3}{7}$, thus, 0<b<1, since, $0$ and thus, as per the general form, the given equation $y= 5.8(\frac{3}{7})^x$ represents exponential decay.

For a better understanding of the explanation provided here, the graph of $y= 5.8(\frac{3}{7})^x$ has been attached. As can be seen from that graph it indeed is an exponential decay.

Answer 2

This represents exponential decay because (3/7) is less than 1