Final answer:
The exponential function y = 7600(0.05)^x can describe a scenario of decay or depreciation. To graph it, label the axes, plot the initial value, and draw a decreasing curve. The decay rate is 5%, affecting the average value over time.
Step-by-step explanation:
The exponential function presented, y = 7600(0.05)^x, can represent a situation where you are observing the decay of a substance or the depreciation of an asset over time. The initial amount is 7600 units, and the decay rate is 5% per time period.
To draw the exponential graph:
- Label the x-axis for the time periods and the y-axis for the value of the function.
- Plot the point where x=0, y=7600, which is the starting value.
- The curve will rapidly decrease as x increases because this is a decay function.
- The decay rate is 0.05 or 5%, and it represents the percentage decrease per time period.
- The mean in this context is referring to the average value or the expected value over time, which is affected by the decay and will trend towards zero.
- To calculate the probability P(x < 0.40), you would identify the x-value where y is less than 0.40, and then shade the area under the curve to the left of this x-value.
Note that without a specific probability distribution or further information, the exact calculation and shading of P(x < 0.40) cannot be completed, but the concept of how to approach this on the graph has been explained.