Question

tell whether the function represents exponential growth or exponential decay. then graph the function.

Answer 1

The function given is:

`y=2e^(-x)`

(a)

The function represents exponential decay. An exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. We can re-write the equation as:

`\begin{gathered} y\text{ = }2e^(-x) \\ y\text{ = 2 }* e^(-x) \\ y\text{ = 2 }*\text{ }(1)/(e^x) \\ =\text{ }(2)/(e^x) \end{gathered}`

Recall that by law of indices:

`a^(-1)\text{ = }(1)/(a)`

As x grows large, the value of y decreases and approaches zero.

(b) The graph of the function is shown below.