Answer:
Correct answer: n = 5.96 ≈ 6 years
Step-by-step explanation:
Given:
Currently population P = 13,000
The percentage annual population growth is 4.5 % or in decimal notation
p = 1.045
Population after n years Pₙ = 16,900
Work:
After first year it will be P₁ = P · p
After second year it will be P₂ = P₁ · p = P · p²
After third year it will be P₃ = P₂ · p² = P · p³
.....................................................................................
After n-th year it will be Pₙ = P · pⁿ
pⁿ = Pₙ / P
n = log p (Pₙ / P) = ln (Pₙ / P) / ln p
n = ln (16,900/ 13,000) / ln 1.045 = ln 1.3 / ln 1.045 = 5.96 ≈ 6
If we accept n = 5.9 we will get:
Pₙ = P · pⁿ = 13.000 · 1.045⁵°⁹ = 16,855
If we accept n = 5.96 we will get:
Pₙ = P · pⁿ = 13.000 · 1.045⁵°⁹⁶ = 16,899.6
If we accept n = 6 we will get:
Pₙ = P · pⁿ = P₆ = P · p⁶ = 13.000 · 1.045⁶ = 16,929.38
What you will accept is yours choice.
God is with you!!!
