Solve the problem.

If certain bacteria are cultured in a medium with sufficient nutrients, they will double in size and then divide every 40 minutes. Let N₁ be the initial number of bacteria cells, N₂ the number after 40 minutes, N₃ the number after 80 minutes, and N_j the number after 40(j - 1) minutes. 

(a) Write N_j+1 in terms of N_j for j ≥ 1.

(b) Determine the number of bacteria after 2 hr if N₁ = 230.

(c) Graph the sequence N_j for j = 1, 2, 3, . . . , 7, where N₁ = 230. Use the window [0, 10] by [0, 15,000].

(d) Describe the growth of these bacteria when there are unlimited nutrients.