Final answer:
The given equation represents exponential growth with a 2.5% growth rate. It is not a probability distribution, hence the task of shading for probability is not applicable. For an exponential distribution with decay, one could graph it and find probabilities by shading areas under its curve.
Step-by-step explanation:
The equation y = 16.5(1.025)^(1/x) suggests that for every increase in x, there is an increase in y, representing exponential growth. The base of the exponential, 1.025, is greater than 1, indicating growth with each step in x. To graph this function, we plot the value of y against x, with the y-axis representing the value of the function and the x-axis the independent variable x. It's not possible to shade an area representing the probability that one student has less than $0.40 in his or her pocket because this is not a probability distribution function.
The growth rate here is given by the base 1.025 and can be converted into a percentage by subtracting 1 and multiplying by 100, resulting in a 2.5% growth rate. As for mean (μ), it is not directly specified in this formula and would typically apply to probability distributions rather than deterministic functional growth described by this equation.
For comparison, let's consider the exponential distribution with a decay rate represented as X~ Exp(0.1). The decay rate here would be 0.1, with the mean (μ) being the reciprocal of the decay rate, which is 10. Graphing the probability distribution function for this exponential distribution, we would find the probability P(x < 6) by shading the area under the curve to the left of x = 6.