( points A city block has 10 pigeons and then 1 week later there are 15 pigeons. Assuming the rate of growth is proportional to the number of pigeons present, what is the differential equation which describes the growth of the pigeon population? Solve this equation to find the equation that describes how many pigeons are present. Let P(t) be the number of pigeons where t is measured in weeks.( points) The CIA published data about foreign countries on its web page. In particular they show total population as well as population growth. If a student is looking at Russia, they will see that the total population of Russia is declining. When they look at the table that shows annual population growth all the rates are positive. Assume population grows and declines at a rate proportional to the population. What is the problem?A radioactive isotope decays over time at a rate proportional to the amount of the material at a given time. A(t) is the amount of material. At t = 0 there is 100 kg and time t = 4 there is 60 kg. Write the particular solution to the differential equation which will describe the amount of isotope after time t.Jane is taking a history class. The teacher states that the population of a cou shrinking at a rate proportional to the population at a given time, and describ size of the population as P = 10e SUP 0.5t SUP, where t is years. Is this possiAssume that the rate of evaporation for water is proportional to the initial amount of water in a bowl. If Jill places 1 cup of water outside and notices that there is 1/2 cup of water 6 hours later. Can she use a differential equation to find when there is no water left?Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If Jill places 1 cup of water (8 ounces) outside and notices that there is 1/2 cup of water 7 hours later. How much water will be left in 9 hours?f a population of is becoming extinct and the population is decaying exponentially. Assume that there are 2,000 animals, and there will only be one animal in 50 years. What is k, the rate of decay?If a population of fruit flies doubles every 3 days. What is k, the proportionality constant