Question

The population of a city was 40960 three years ago. If its present population is 49130find the annual rate of growth of population.

Answer 1

Answer:

6.25%

Step-by-step explanation:

Initial population = 40960

Period = 3 years

Final Population = 49130

Define r:

Let the growth rate be r

Solve r:

49130 = 40960 ( 1 + r)³

( 1 + r)³ = 49130/40960

1 + r = ∛(49130/40960)

1 + r = 1.0625

r = 1.0625 - 1 = 0.0625 = 6.25%

Answer: The growth rate is 6.25%

Answer 2

Answer : $\bold{Rate \: of \: growth \: = \: 6.25 \%}$



Explanation -


Given :

Population 3 years ago = 40960

Time = 3 years

Present Population = 49130


Let the rate of growth = r

Solving r -


$49130 = 40960( {1 + r)}^{3}$


$( {1 + r})^{3} = \dfrac{49130}{40960}$



$( {1 + r})^{3} = \dfrac{4913}{4096}$


$( {1 + r)}^{3} = ( \frac{17}{16} ) ^{3}$


$( 1 + r) = \dfrac{17}{16}$


$1 + r = 1.0625$

$r = 1.0625 - 1$


$r = 0.0625$


$r = 0.0625 \times 100$


$rate \: = 6.25\%$



Hence :

$\bold{Rate \: of \: growth \: = \: 6.25 \%}$