Question

The population of a new city is 1 million and is growing at 20% annually. How many years would it take to triple at this growth rate ? O 3-4 years O 4-5 years O 5-6 years O 6-7 years​

Answer 1

Answer:

${4}^{th} option \: \: 6 - 7 \: \: years.$

Step-by-step explanation:

Let the present population (P) = 1M, After n years, population will be tripled.

i.e. A = 3P

Using the formula,

$A \: = P \: {(1 \: + \: \frac{r}{100} \: ) }^{n}$

$3P \: = { \: P(1 \: + \frac{20}{100}) }^{n}$

=

$3 = ( { \frac{6}{5}) }^{n}$

=

$log(3) = \: n \: log( \frac{6}{5} )$

=

$n \: = \frac{ log(3) }{ log(1.2) }$

$n \: = \frac{0.4771}{0.0792}$

$n \: = 6.02 \: \: years \: approx$

Hence, 4th option 6 - 7 years is correcr.