Answer:
27 years.
Step-by-step explanation:
2000->100%
?->3.5%
=70 people growth each year
3900-2000=1900[expected growth]
70-per year
1900-?
1900*1/70=27.1
=27.|1
27 years
It will take 9 years for the town's population to reach 3900.
"An exponential function is a function of form f (x) = a^(x), where a is the base."
f(x) = a×(1+r)^x
where,
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
For given situation,
initial population: a = 2000,
growth rate r = 3.5/100
⇒ r = 0.035
f(x) = 3900
We need to find the nearest year to reach the population 3900.
i.e., to find value of x(years)
Using the exponential growth function,
⇒ 3900 = 2000(1 + 0.035)^x
⇒ 3900/2000 = (1.035)^x
⇒ 1.95 = (1,035)^x
⇒ [tex]x=log_{1.035} 1.95[/tex]
⇒ x = 19.41
⇒ x ≈ 19
Therefore, it will take 19 years to reach 3900.
Learn more about exponential growth here:
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