In the given problem, apply your knowledge in algebra and basic mathematics specially in solving word problem about exponential growth.
Given
On day 6, a plant was 3 cm tall.
On day 20, it was 15 cm Tall.
1. Find the rate of growth.
Growth = P(1+r)^t
3 = P(1+r)⁶ → P = (1+r)⁶/3
15 = P(1+r)²⁰ → P = (1+r)²⁰/15
(1+r)²⁰/15 = (1+r)⁶/3
15(1+r)⁶ = 3(1+r)²⁰
(1+r)¹⁴ = 5
(1+r) = 1.12
r = 0.12
r = 12%
2. write an equation of the relationship.
Growth = P(1+r)^t
Find P
3 = P(1+0.12)⁶
P = 3/(1+0.12)⁶
P = 1.52
Growth = 1.52(1+0.12)^t
Check
when t = 6, growth = 3
3 = 1.52(1+0.12)⁶
3 = 3 ✓
when t = 20, growth = 15
15 = 1.52(1+0.12)²⁰
15 = 14.66
15 = 15 ✓
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