Question

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

Answer 1

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

Answer 2

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((3)/(7))^x`

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

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