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!!!
Answer: it will take 6 years until the population will reach 16900
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^ t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
A = 16900
P = 13000
r = 4.5% = 4.5/100 = 0.045
Therefore
16900 = 13000(1 + 0.045)^t
16900/13000 = (1.045)^t
1.3 = (1.045)^t
Taking log of both sides to base 10
Log 1.3 = log1.045^t = tlog1.045
0.114 = 0.0191t
t = 0.114/0.0191
t = 6.0 years to the nearest tenth
