Math Problem Statement

Evaluate the following expression for xequals20. 8000 left parenthesis 1.08 Superscript x right parenthesis Question content area bottom Part 1 8000 left parenthesis 1.08 Superscript x right parenthesisequals    enter your response here ​(Do not round until the final answer. Then round to two decimal places as​ needed.)

Solution

The value of the expression 8000×(1.0820)8000 \times (1.08^{20}) is approximately 37,287.66 when rounded to two decimal places.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How does changing the base from 1.08 to another value affect the result?
  2. What happens if x=25x = 25 in the same expression?
  3. Can you express 1.08x1.08^x as a logarithmic equation and solve for xx?
  4. How would this expression behave if the exponent xx were negative?
  5. What is the relationship between compounding interest and this type of exponential growth?

Tip: In exponential expressions, small changes in the exponent can lead to large variations in the result due to the power function.

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Algebra

Formulas

Exponential expression: a(b^x)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-12