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Aloiza [94]
3 years ago
8

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

triple​?
Mathematics
1 answer:
Lisa [10]3 years ago
8 0

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

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