Question

The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less than 12,000?

Answer 1

Answer:

After 2 years the population will be 12000 or less than 12000

Step-by-step explanation:

Tip

• The term “population” encompasses a group of organisms of a single species that can interbreed and live in the same time in the same environment.

Formulae Used

By using the equation $Y=a*(1-rate)^{time}$

Given

Y=the future value 12000

a=starting value 13000

rate=5%

Find

After how many years the population will be 12000 or less than 12000

Solution

By using formulae $Y$=$a*(1-rate)^{time}$

$12000=13000*(1-0.05)^{x} \\\frac{12000}{13000} =0.95^{x}$

Use the natural log function

$x=In(12/13)/In(0.95)\\x=1.56 years$

Approx 2 years

Final Answer

After 2 years the population will be 12000 or less than 12000

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Answer 2

Answer:

1.6 years i.e. 1 year 6 months.

Step-by-step explanation:

Given:- Current population = 13,000

            Rate of decrease in population = 5%

To Find:- Number of years in which population will be less than 12,000.

Solution:-

Present Population, P = 13,000

Rate  = -5% since it's decreasing.

Population after n years = $P(1+\frac{r}{100} )^{n}$

⇒ $12000 = 13000 (1+\frac{(-5)}{100} )^{n}$

⇒ $\frac{12}{13} = (1-\frac{1}{20} )^{n}$

⇒ $\frac{12}{13} =(\frac{20-1}{20} )^{n}$

⇒ $\frac{12}{13} = (\frac{19}{20}) ^{n}$

⇒ $ln(\frac{12}{13}) = n (ln(\frac{19}{20} ))$

⇒ $ln 12-ln 13 = n(ln19-ln20)$

⇒ $2.485 - 2.565 = n(2.945-2.995)$

⇒ $-0.08 = -0.05n$

⇒ $n = \frac{0.08}{0.05}$

⇒ $n = 1.6$

Therefore, population will be less than 12,000 after 1.6 years.

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