Math Problem Statement

solve

100(exp(-0.297) - 1) =

Solution

The result of the expression 100(exp(0.297)1)100(\exp(-0.297) - 1) is approximately 25.70-25.70.

Would you like more details or have any questions?

Here are five related questions for further practice:

  1. How would the result change if the exponent was positive, i.e., exp(0.297)\exp(0.297)?
  2. Can you calculate 100(exp(0.5)1)100(\exp(-0.5) - 1)?
  3. How does the value of exe^{-x} behave as xx increases?
  4. How would the expression change if multiplied by a factor other than 100?
  5. What is the derivative of f(x)=100(exp(x)1)f(x) = 100(\exp(-x) - 1)?

Tip: The function exp(x)\exp(-x) is used often in decay models and approaches 0 as xx increases.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Algebra

Formulas

Exponential function: exp(x) = e^x
Basic algebraic manipulation: 100(exp(-x) - 1)

Theorems

None

Suitable Grade Level

Grades 11-12, College level