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Bacterial Growth. Suppose that a biologist performs an experiment in which he or she measures the rate at which a specific type of bacterium reproduces asexually in different culture media. The experiment shows that in Medium A the bacteria reproduce once every 60 minutes, and in Medium B the bacteria reproduce once every 90 minutes. Assume that a single bacterium is placed on each culture medium at the beginning of the experiment. Write a program that calculates and plots the number of bacteria present in cach culture at intervals of 3 hours from the beginning of the experiment antil 24 hours have elapsed. Make two plots, one a linear xy plot and the other a linear-log (semi logy) plot. How do the numbers of bacteria compare on the two media after 24 hours?

Declbels. Engineers often measure the ratio of two power measurements in decibels, or dB. The equation for the ratio of two power measurements in decibels is $$ d B=10 \log _{10} \frac{P_{2}}{P_{1}} $$ where \(P_{2}\) is the power level being measured, and \(P_{1}\) is some reference power level. Assume that the reference power level \(P_{1}\) is 1 watt, and write a program that calculates the decibel level corresponding to power levels between 1 and 20 watts, in \(0.5 \mathrm{~W}\) steps. Plot the dB-versus- power curve on a log-linear scale.

Harmonic Mean. The harmonic mean is yet another way of calculating a mean for a set of numbers. The harmonic mean of a set of numbers is given by the equation $$ \text { harmonic mean }=\frac{N}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\ldots+\frac{1}{x_{N}}} $$ Write a MATLAB program that will read in an arbitrary number of positive input values and calculate the harmonic mean of the numbers. Use any method that you desire to read in the input values. Test your program by calculating the harmonic mean of the four numbers \(10,5,2\), and \(5 .\)

Mean Time Between Failure Calculations. The reliability of a piece of electronic equipment is usually measured in terms of mean time between failures (MTBF), where MTBF is the average time that the piece of equipment can operate before a failure occurs in it. For large systems containing many pieces of electronic equipment, it is customary to determine the MTBFs of each component and to calculate the overall MTBF of the system from the failure rates of the individual components. If the system is structured like the one shown in Figure 4.6, every component must work in order for the whole system to work, and the overall system MTBF can be calculated as $$ \mathrm{MTBF}_{\mathrm{yy}}=\frac{1}{\frac{1}{\mathrm{MTBF}_{1}}+\frac{1}{\mathrm{MTBF}_{2}}+\ldots+\frac{1}{\mathrm{MTBF}_{n}}} $$ Write a program that reads in the number of series components in a system and the MTBFs for each component, and then calculates the overall MTBF for the system. To test your program, determine the MTBF for a radar system consisting of an antenna subsystem with an MTBF of 2000 hours, a transmitter with an MTBF of 800 hours, a receiver with an MTBF of 3000 hours, and a computer with an MTBF of 5000 hours.