%5E10.jpeg "(1+0 05)^10")
Evaluating the Expression: (1 + 0.05)^10
In mathematics, evaluating expressions with exponents can be a daunting task, especially when dealing with decimals. In this article, we will explore the evaluation of the expression (1 + 0.05)^10.
Understanding the Expression
The given expression is (1 + 0.05)^10, where 1 is the base and 0.05 is the decimal value being added to it. The exponent 10 indicates that the result of the addition should be raised to the power of 10.
Breaking Down the Expression
To evaluate this expression, we need to follow the order of operations (PEMDAS):
- Addition: Calculate
1 + 0.05first, which gives us1.05. - Exponentiation: Raise
1.05to the power of10, denoted as(1.05)^10.
Calculating the Result
To calculate (1.05)^10, we can use a calculator or perform the calculation manually. The result is approximately:
(1.05)^10 ≈ 1.6289
Interpretation
The result of (1 + 0.05)^10 is approximately 1.6289. This value can be interpreted in various contexts, such as:
- Compound Interest: If
1represents the principal amount, and0.05represents the interest rate, then(1 + 0.05)^10calculates the future value of the investment after10periods. - Growth Rate: The result can also be seen as the growth rate of a quantity that increases by
5%every period, resulting in a cumulative growth of approximately62.89%over10periods.
In conclusion, evaluating the expression (1 + 0.05)^10 requires careful attention to the order of operations and can have significant implications in various mathematical modeling contexts.
