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Chapter 6: Problem 3

Explain the meaning of doubling time.

Short Answer

Expert verified
Answer: Doubling time is the amount of time it takes for a quantity or population to double in size, given a constant growth rate. It helps in understanding how quickly the population or investment is growing due to compounding over time. To estimate the doubling time, we can use the "Rule of 70", which involves dividing 70 by the growth rate (as a percentage).

Step by step solution

01

Introduction to Exponential Growth

Exponential growth occurs when the growth rate of a quantity is proportional to its current size. This is commonly seen in populations or investments where the larger the quantity; the more significant the growth in absolute terms. This kind of growth can be affected by things like interest rates and reproduction rates.
02

Defining Doubling Time

Doubling time is the amount of time it takes for a quantity or population to double in size, given a constant growth rate. It helps in understanding how quickly the population or investment is growing due to compounding over time.
03

Calculating Doubling Time Using the Rule of 70

To estimate the doubling time, we can use the "Rule of 70" 鈥� a simple formula based on exponential growth. \[ Doubling\ Time \approx \frac{70}{Growth\ Rate\ in\ \%} \] When the growth rate is given as a percentage, we can divide 70 by the growth rate to estimate the doubling time.
04

Example of Doubling Time Calculation

Let's take an example of a population with a growth rate of 2% per year. To calculate the doubling time, we can use the Rule of 70: \[ Doubling\ Time \approx \frac{70}{2\%} \] \[ Doubling\ Time \approx \frac{70}{2} \] \[ Doubling\ Time \approx 35 \ years \] So, the population will approximately double in size in about 35 years, given a constant growth rate of 2%.
05

Conclusion

Doubling time is a concept that helps us understand how quickly a quantity or population is growing due to its constant growth rate. We can estimate the doubling time using the Rule of 70, which is a simple way to understand how long it takes for the quantity to double based on the given growth rate.

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Most popular questions from this chapter

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