The function given is:
[tex]y=2e^{-x}[/tex]
(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:
[tex]\begin{gathered} y\text{ = }2e^{-x} \\ y\text{ = 2 }\times e^{-x} \\ y\text{ = 2 }\times\text{ }\frac{1}{e^x} \\ =\text{ }\frac{2}{e^x} \end{gathered}[/tex]
Recall that by law of indices:
[tex]a^{-1}\text{ = }\frac{1}{a}[/tex]
As x grows large, the value of y decreases and approaches zero.
(b) The graph of the function is shown below.
