Respuesta :
18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.
Step-by-step explanation:
The given is,
Population of 4000
Rate of grow 3.5% every year
Population after few years 7500
Step:1
Formula to calculate the population with the grow rate every year,
[tex]F=P(1+r)^{t}[/tex]..........................(1)
Where,
F - Population after t years
P - Initial population
r - Rate of grow
t - No.of years
From given,
F = 7500
P = 4000
r = 3.5%
Equation becomes (1),
[tex]7500=4000(1+0.035)^{t}[/tex]
[tex]\frac{7500}{4000} = (1+0.035)^{t}[/tex]
1.875 = [tex](1+0.035)^{t}[/tex]
[tex]1.875 = (1.035)^{t}[/tex]
Take log on both sides,
[tex]log 1.875 = (t)log 1.035[/tex]
Substitute log values,
[tex]0.2730= (t) 0.014940349[/tex]
[tex]t = \frac{0.273}{0.014940349}[/tex]
= 18.273
t = 18.273 year
or
t = 18 years 3 months 2 weeks
Result:
18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.
Answer:
18 years is the answer
Step-by-step explanation:
