Pollution levels in a lake have been modeled by the equation

Question

Pollution levels in a lake have been modeled by the equation x = 0.04 + 0.19e^-0.37t

Where x is the volume of pollutants (in cubic kilometers) and t is the time (in years). What is the rate of change of x with respect to time? 

x^'(t) = ?

Answer 1

Answer 2

This is simply a derivation problem. Derive the equation and you will have the rate of change with respect to time. The derivative is a rate function (spatial measurement per time ie: volume/second)

The derivation of e^x is e^x. because d/dx e^x=1*e^x.

The derivation of e^x is is the multiplication of the derivative of the numerator to the base equation