## Write a difference equation for the population at the beginning of the nth day after January 1, 2000 with the immigration rate as the excitation of the system.

At the beginning of the year 2000, the country Freedonia had a population p of 100 million people. The birth rate is 4% per annum and the death rate is 2% per annum, compounded daily. That is, the births and deaths occur every day at a uniform fraction of the current population and the next day the number of births and deaths changes because the population changed the previous day. For example, every day the number of people who die is the fraction  0.02/365  of the total population at the end of the previous day (neglect leap-year effects). Every day 275 immigrants enter Freedonia.

(a) Write a difference equation for the population at the beginning of the nth day after January 1, 2000 with the immigration rate as the excitation of the system.

(b) By finding the zero-excitation and zero-state responses of the system determine the population of Freedonia at the beginning of the year 2050.

### Calculate the maximum achievable bridge out-of-balance voltage for an applied torque T of 103 N m given the following

Four strain gauges, with specification given below, are available to measure the torque on a cylindrical shaft 4 cm in diameter connecting a motor and load. (a) Draw clearly labelled….

### Find the gain and phase characteristics of the maintaining amplifier.

A solid-state capacitive humidity sensor has a capacitance given by: C = 1.7 RH + 365pF where RH is the percentage relative humidity. The sensor has an associated parallel resistance….

### calculate the mean velocity of the gas at maximum flow rate

A pitot tube is used to measure the mean velocity of high pressure gas in a 0.15 m diameter pipe. At maximum flow rate the mean pitot differential pressure is….