Question

If the population of a particular country is growing at 3.2 % compounded​ continuously, how long will it take the population to triple​?

Answer 1

Answer:

It will take 34.33

Step-by-step explanation:

* Lets talk about the compound continuous growing

- Compound continuous growing can be calculated using the formula:

 $A=Pe^{rt}$

# A = the future value

# P = the initial amount

# r = the growing rate  in decimal

# t = the time

* Lets solve the problem

- The population of a particular country is growing at 3.2 %

 compounded​ continuously

∴ r = 3.2/100 = 0.032

- We need to find how long will it take the population to triple​

∵ The initial population is P

∴ A = 3P

∵ $A=Pe^{rt}$

∴ $3P=Pe^{0.032t}$

- Divide both sides by P

∴ $3=e^{0.032t}$

- Insert ㏑ for both sides

∴ $ln(3)=ln(e^{0.032t})$

- Remember $ln(e^{n})=n$

∴ ㏑(3) = 0.032t

- Divide both sides by 0.032

∴ t = ㏑(3)/0.032 = 34.33

* It will take 34.33