Power PlayClass 8 Mathematics Case Study Questions

In a science class, students explore the concept of exponential growth by folding a sheet of paper. They start with a standard A4 sheet, which has a thickness of approximately $0.1$ mm, or $10^{-4}$ meters. The students are told that it is physically impossible to fold a piece of paper more than 7 or 8 times. However, they are asked to imagine a magical sheet of paper that can be folded as many times as they wish. With each fold, the thickness of the paper doubles. The class decides to calculate how thick the paper would become after a certain number of folds and compare it to real-world objects. They are curious to see how quickly the thickness grows from something barely visible to astronomical heights.

Estu and Roxie are learning about digital security. They discover that the strength of a password depends on its length and the variety of characters used. They analyze two types of locks. The first is a simple numeric lock that uses a 5-digit password, where each digit can be any number from 0 to 9. The second is an alphanumeric lock that uses a 4-character password, where each character can be any of the 26 uppercase letters (A-Z) or any of the 10 digits (0-9). They want to use exponents to represent the total number of possible passwords for each lock and compare their security.

A science documentary presents fascinating facts about our solar system. It uses scientific notation to express vast distances. The average distance from the Sun to Earth is approximately $1.496 \times 10^{11}$ meters. The distance from the Sun to Saturn is about $1.43 \times 10^{12}$ meters. Light travels at a constant speed of approximately $3 \times 10^8$ meters per second. Students are asked to use these figures to compare distances and calculate travel times for light, applying their knowledge of exponents and scientific notation. This helps them appreciate the immense scale of space and the utility of scientific notation in handling such large numbers.