Question: 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.

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₊₁in terms of N_j for j ≥ 1.

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

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

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