Final answer:
To graph the given exponential function, label the axes and plot a rising curve since it represents exponential growth.
Step-by-step explanation:
To graph the function f(t) = e^0.4t, begin by labeling the x-axis as the time variable (t) and the y-axis as the function value (f(t)). Since the function represents an exponential growth, the graph will show a rising curve as we move from left to right. The decay rate is not applicable here because the function is growing, not decaying. However, if we consider a similar function with a negative exponent, such as f(t) = e^-0.4t, then it would have a decay rate of 0.4 and the graph would depict a declining curve. The mean of a probability distribution, denoted as m, would be the peak value on the y-axis for a decaying exponential probability function.
When graphing f(t) = e^0.4t, there is no maximum value for f(x) as the function approaches infinity as t grows. If we are to shade the area representing the probability P(x < 0.40), we would actually need the context of a probability density function (PDF) which is different from the given exponential function. In the absence of a PDF, we cannot shade an area under the curve of f(t) = e^0.4t to represent a probability.
If we were to discuss the given examples with other functions and data, such as the wave functions and the quadratic equations, we could label and analyze various properties such as amplitude, wave speed, and solve for roots using the quadratic formula, but those analyses would be specific to the functions presented in the examples provided.