Can you explain the inequalities in exponential functions?

In summary, exponential inequalities are mathematical expressions involving exponential functions and inequality symbols. They can be solved using rules of exponents and algebraic techniques. These inequalities have various applications in fields such as finance, biology, physics, and chemistry. To graph them, one can use a calculator or manually plot points and shade the region that satisfies the inequality. Some common mistakes when dealing with exponential inequalities include incorrect order of operations, misapplying logarithms, and misinterpreting the solution set.
  • #1
stukbv
118
0
Hello, could somebody please explain to me how

1-exp(-μt) ≤ μt

and similarly

(1-exp(-μt))exp(-λt) ≥ μt-μ2t2\2)(1-λt)

Thanks a lot
 
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  • #2
You haven't said what you want explained...
 
  • #3
Sorry, I just want to know why they're true, they are in my lecture notes and I can't work out why we know these inequalities hold.
 

FAQ: Can you explain the inequalities in exponential functions?

What are exponential inequalities?

Exponential inequalities are mathematical expressions that involve exponential functions and inequality symbols, such as <, >, ≤, and ≥.

How do you solve exponential inequalities?

To solve exponential inequalities, you can use the rules of exponents and algebraic techniques such as isolating the variable, factoring, and using logarithms.

What are the applications of exponential inequalities?

Exponential inequalities are used to model and solve real-world problems in fields such as finance, biology, physics, and chemistry.

How do you graph exponential inequalities?

To graph exponential inequalities, you can use a graphing calculator or manually plot points and shade the region that satisfies the inequality.

What are some common mistakes when dealing with exponential inequalities?

Some common mistakes when dealing with exponential inequalities include forgetting to use the correct order of operations, incorrectly applying logarithms, and misinterpreting the solution set.

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