Question

The population of a town is increasing at a rate of 6.2% per year. The city council believes they will have to add another elementary school when the population reaches 100,000. If there are currently 76,000 people living in the town, how long do they have before the new school will be needed?

Answer 1

Answer:

The correct solution is "4.6".

Step-by-step explanation:

Given:

Interest rate,

r = 6.2%

or,

 = 0.062

Amount,

A = 100000

Principle,

P = 76000

As we know,

⇒ $A=P(1+\frac{r}{100} )^n$

On substituting the values, we get

⇒ $100000=76000(1+\frac{6.2}{100} )^n$

⇒ $(1+0.062)^n=\frac{100}{76}$

On taking log both sides, we get

⇒ $n \ log_e(1.062)=log_e(\frac{100}{76} )$

⇒                   $n=\frac{ln(\frac{100}{76} )}{ln(1.062)}$

By putting the values of log, we get

⇒                      $=4.5622$

or,

⇒                      $=4.6$