To solve these problems you can make use of numpy, matplotlib.

The kidneys remove 20% of a drug every 4 hours. Assume a patient takes an initial dose of the drug followed by a dose of the drug of 20mg every 4 hours.

Let d0 denote the initial amount of the drug

For each of the following initial values 140mg 70mg 100mg

Determine the amount of drug in the blood in 20 hours and 2days.

For instance: dn+1 = dn-20%ofd +20 = 0.8dn+20, d1=d0*.8+ 20 = 140*0.8 +20 = 132

1. Determine the amount for the first five time periods (do this in several steps) You should get 132.0, 125.60000000000001, 120.48000000000002, 116.38400000000001, 113.10720000000002b. Write a function that generates an array or list of the amounts for n time for a given initial value periods.c. Use this function to determine three sequences of values for each of the initial valuesd. Plot the three sequences you should get one that is the equilibrium the amount of drug stays constant

2. Assume the annual growth rate of deer is 4% and the state restricts hunting to 8000 per year. Let P0 be the population in 2010 and Pn the population in n years after 2010.

3. Model this using the same method in #1.

4. Use the following initial populations: 250000, 150000, 200000.

5. Plot the three sequence of populations is there an equilibrium?

THANKS FOR YOUR HELP!