# Investigation 20 Doubling Time Exponential Growth Answer Key.zip

## Investigation 20: Doubling Time and Exponential Growth - Zip File with Answers

Do you want to learn about the mathematical concept of exponential growth and how it applies to biological and other processes? Do you want to download the zip file with the answer key for investigation 20: doubling time and exponential growth? If so, you are in the right place. In this article, we will explain what exponential growth and doubling time are, why they are important, and how to solve investigation 20 using these concepts. We will also provide you with a link to download the zip file with the answer key for investigation 20.

## investigation 20 doubling time exponential growth answer key.zip

## What is exponential growth?

Exponential growth is a type of growth that occurs when a quantity increases by a fixed percentage per unit of time. For example, if a population grows by 3% per year, it means that every year it increases by 3% of its previous size. This means that the population grows faster and faster as it gets bigger. The graph of exponential growth looks like a curve that rises steeply (see Figure 1).

Figure 1: An exponential curve

Exponential growth can be found in many situations, such as money in the bank, population growth, bacteria growth, resource consumption, etc. Exponential growth can be beneficial or harmful depending on the context. For example, exponential growth in your investments is welcome, but exponential growth in human population or infectious diseases can have grave implications.

## What is doubling time?

Doubling time is the time it takes for a quantity that grows exponentially to double in size. For example, if a population grows by 3% per year, it means that every year it increases by 3% of its previous size. This means that after a certain amount of time, the population will be twice as big as it was before. This amount of time is called the doubling time.

Doubling time is a useful way to measure and compare the rate of exponential growth. The higher the percentage growth rate, the shorter the doubling time. For example, if a population grows by 4% per year, its doubling time is shorter than if it grows by 2% per year.

There is a simple formula to estimate the doubling time for any percentage growth rate. It is called "the rule of 70". To use this rule, you just need to divide the number 70 by the percentage growth rate. For example, if a population grows by 3% per year, its doubling time is about 23 years (70/3 = 23). If a population grows by 10% per year, its doubling time is about 7 years (70/10 = 7).

## How to solve investigation 20: doubling time and exponential growth?

Investigation 20: doubling time and exponential growth is an exercise that explores the effects of exponential growth in two scenarios: one involving money and one involving bacteria. In both scenarios, you need to use the concepts of exponential growth and doubling time to calculate and compare different outcomes.

In scenario A, you need to compare two payment methods for a job: one that pays $20 per hour and one that pays one penny for the first day, then doubles to two cents the next day, four cents the third day, and so on for a month. You need to show your work, including intermediate calculations, and answer some questions about which method is better for whom, when does the employee break even, what is the total difference between the two methods over the month, etc.

In scenario B, you need to model the growth of bacteria in a can of strawberry syrup under ideal conditions. You need to assume that the bacteria double their numbers every 20 minutes and that they start with a few bacteria at 6 A.M. You need to calculate how many bacteria there will be at different times of the day until they run out of food at 6 P.M. You also need to answer some questions about how fast the bacteria grow, how much space they occupy, what factors might limit their growth, etc.

Where to download the zip file with the c481cea774