Question

create a sequence to show exponential growth where the poplutaion of 120 is doubling everyday

Answer 1

You can describe this exponential growth with either a recursive rule or an explicit formula.

Recursive:
- a0 = 120 (population at day 0)
- a_{n+1} = 2 · a_n

Explicit (closed form):
- If you call the initial day day 0: a_n = 120 · 2^n
- If you call the initial day day 1: a_n = 120 · 2^{\,n-1}

First few terms (starting at day 0):
- Day 0: 120
- Day 1: 240
- Day 2: 480
- Day 3: 960
- Day 4: 1,920
- Day 5: 3,840
- Day 6: 7,680
- Day 7: 15,360

Examples:
- After 10 days: a_10 = 120·2^{10} = 120·1024 = 122,880
- After 30 days: a_30 = 120·2^{30} ≈ 128,849,018,880

This shows the characteristic rapid (exponential) growth: the population doubles each day.