EXERCISES1. Find the first 5 terms of the sequence defined by the recurrence relation and the initial condition: ,41nnaa 10a2. Find a solution to the recurrence relation ,31nnaa 100a. Use an iterative approach.3. A person deposits $1200 in an account that yields 8.5% interest compounded yearly. a) Set up a recurrence relation for the amount in the account at the end of n yearsb) Find an explicit formula for the amount in the account at the end of n yearsc) How much will the account have after 12 years?3. Assume the population of the world in 2000 is 5.9 billion and is growing at the rate of 1.27% a year.a) Set up a recurrence relation for the population n years after 2000.b) Find an explicit formula for the population n years after 2000.c) What will the population of the world be in 2020?4. Solve the recurrence relations:a)5 ,3 ,2for 61021aanaaannnb)2 ,2 ,2for 1071021aanaaannnc)10 ,3 ,2for 861021aanaaannn5. Consider the discrete logistic recurrence relation 1 ),1(11nxrxxnnn. Use Maple to do the following:a) Compute 200x with 5.01x and 31  r. Do the results support the conjecture thatx always exists and is an increasing function of r?b) Repeat with 55.3 ,25.3 ,1.3  rrr. Describe your observations.c) Use 1.39.2  r to determine as closely as possible just where the single limiting population splits into a cycle of period 2.d) Find the period of cycle obtained with growth rates of 365.3r, and 57.3r.6. Suppose we have a population of critters who never grow past five years old. Suppose, further, that 80% of the critters survive each year to move onto the next age class, with the exception of the five year old critters which always die. If newborns and yearlings have no offspring, and if middle aged critters (2, 3 and 4 year olds) have, on average, 0.35 newborns each year, while the oldest critters (5 year olds) have only 0.1 newborns on average. The initial population consists of sixty critters evenly spread throughout the six age classes. Determine the population distribution 10 years into the future.7. The following table gives the population of females in six specific age groups of asmall woodland mammal.Table 1: Female Population of Small WoodlandMammalsAge (in months)0-3 3-6 6-99-1212-15 15-18Number of Females14 8 12 4 0 0Table 2: Birth, and Survival Rates for Each AgeGroupAge (in months)0-3 3-6 6-9 9-1212-1515-18Birth Rate 0 0.3 0.8 0.7 0.4 0Survival Rate 0.6 0.9 0.9 0.8 0.6 0Find the population after 12