Answer:
Step-by-step explanation:
The equation is: 2400 = 7200e ^ (-0.2x)
Here's why there is no solution:
Exponential growth vs. decay: The term e ^ (-0.2x) represents an exponential decay function. As x increases, the value of the exponent becomes more negative, and the term e ^ (-0.2x) approaches zero but never reaches zero itself.
Constant value: The left side of the equation, 2400, is a constant positive value.
Since an exponential decay function approaches zero but never reaches it, there is no value of x for which 7200e ^ (-0.2x) will be equal to the constant value 2400.
Therefore, the equation has no solution. The answer is: The exact solution set is {} (empty set).