Please explain step by step on how and why you did the question below the way you did them and how I can apply it to other questions in the same concept below is questions about Discrete-time Dynamic Systems (DTDS)

o 4 o Question 2: Assume that the dynamics of caffeine absorption are given by y, = 0.87C, where is time in hours and C, is the concentration of caffeine. If C\\y = 1000, estimate the time needed for 80% of the caffeine to be eliminated from the body (i.e. 20% left). What if Co = 5007 Question 3: A population of rabbits is growing at a rate of 10% per year. Write down the discrete dynamical system that describes the evolution of the rabbit population. If the population is initially 1000, how many years will it take for the population to exceed 1000007 Question 4: A city is growing at a rate of 1% per year and initially has 1,000,000 individu- als. What will be the population in 50 years' time? Question 5: Suppose that a patient receives a daily dose of 50mg/L of a certain drug such that 42% of it is eliminated from the body each day. If on a certain Monday, the concen- tration of the drug measured in their body (shortly after the daily dose) is 55 mg/L, write down the Discrete-Time Dynamical System describing the dynamics of the concentration z, of the drug in the body (in mg/L, t days after that Monday). Then write down the general solution to this DTDS