Question

What is the nature of the graph:

$y=6e^{-4x}$

• A. monotonically increasing
• B. monotonically decreasing
• C. Increasing then decreasing
• D. decreasing then increasing

Answer 1

The correct option is B monotonically decreasing

$y=6e^{-4x}$

$y^{\prime }=-24e^{-4x}$

We know that

$e^{-4x}>0$ for all $xϵR$.

Hence

$y^{\prime }<0$ for all $xϵR$.

Therefore the function has a decreasing slope,

Hence the function is a monotonically decreasing exponential function.