(1-0.15)^10

Suzhoumeite

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Jul 03, 2024

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(1-0.15)^10: Understanding the Calculation and Its Real-World Applications

Introduction

In mathematics, exponentiation is a fundamental operation that plays a crucial role in various fields, including algebra, calculus, and statistics. One interesting calculation that involves exponentiation is (1-0.15)^10, which may seem simple at first glance but has significant implications in real-world applications. In this article, we will delve into the calculation, explore its meaning, and discuss its practical uses.

The Calculation

To evaluate (1-0.15)^10, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: 1 - 0.15 = 0.85
2. Raise 0.85 to the power of 10: 0.85^10 = 0.19687 (approximately)

So, (1-0.15)^10 is approximately equal to 0.19687.

Understanding the Result

The result, 0.19687, represents the value of (1-0.15)^10. But what does it mean? To understand this, let's put it into context.

Imagine you have an investment that yields a 15% annual return. To find the net return, you would subtract the return from 1 (100%), resulting in 0.85 (85%). Now, if you want to calculate the net return over 10 years, you would raise 0.85 to the power of 10, which gives you approximately 0.19687.

Real-World Applications

The calculation (1-0.15)^10 has practical implications in various fields:

Finance

• Compound Interest: The result represents the net return on an investment with a 15% annual return over 10 years.
• Discounted Cash Flow: The calculation is used to determine the present value of future cash flows.

Probability

• Survival Rate: In actuarial science, the result can be used to calculate the probability of survival over 10 years given a 15% annual mortality rate.

Biology

• Population Growth: The calculation can be applied to model population growth or decline over 10 years with an annual growth rate of 15%.

Conclusion

In conclusion, (1-0.15)^10 may seem like a simple calculation, but it has far-reaching implications in various fields. Understanding the calculation and its applications can help us make informed decisions in finance, probability, biology, and other areas.