20.) A certain protected species normally doubles its population each month. The initial population is 20, but by the beginning of next month, 1 specimen has died of an infection. In successive months, the infection kills 2, then 4, then 8 and so forth

a. Write a recurrence relation for the size of the population at the beginning of the month n

b. Solve this recurrence relation

c. What is the size of the population at the beginning of month 7?

- Show all of your work (Including your assumptions and mathematical steps)

-"Guess, Expand and Verify" method solution should be verified using Mathematical Induction. Mathematical Induction proof steps should have a basis step, Inductive hypothesis and Inductive step with its proof.

-Write Closed form solution formula with the coefficients before you start the proof.

(Two people have already answered this question for other people but they both got different answers, 1360 and 2112 for c and idk who is right so if someone could re-work through a, b, and c that would be awesome thank you so much!)