What is the formula for continuous compounding?

The formula for continuous compounding is $$A = Pe^{rt}$$ , where $$A$$ is the amount of money accumulated after time $$t$$ , $$P$$ is the principal amount, $$r$$ is the annual interest rate, and $$t$$ is the time in years.

How do you solve $$e^{(x-2)} = 8$$ ?

To solve $$e^{(x-2)} = 8$$ , take the natural logarithm of both sides: $$x - 2 = \text{ln}(8)$$ , then solve for $$x$$ : $$x = 2 + \text{ln}(8)$$ .

What is the formula for compound interest?

The formula for compound interest is $$A = Pigg(1 + \frac{r}{n}igg)^{nt}$$ , where $$A$$ is the amount, $$P$$ is the principal, $$r$$ is the annual interest rate, $$n$$ is the number of times interest is compounded per year, and $$t$$ is the number of years.

What does it mean for an investment to double?

An investment doubles when its final amount $$A$$ is twice the initial principal $$P$$ , i.e., $$A = 2P$$ .

How do you find the time it takes for an investment to double with continuous compounding?

To find the time for an investment to double with continuous compounding, use the formula: $$t = \frac{\text{ln}(2)}{r}$$ , where $$r$$ is the annual interest rate.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

How do you solve $$9^{(3x-5)} = 81^{(3x-2)}$$ ?

To solve $$9^{(3x-5)} = 81^{(3x-2)}$$ , express both sides with the same base: $$9 = 3^2$$ and $$81 = 3^4$$ , then equate the exponents.

What is the significance of the number 'e' in exponential functions?

The number 'e' (approximately 2.718) is the base of natural logarithms and is significant in continuous growth or decay processes, such as compound interest.

Solving Exponential and Logarithmic Functions Q Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is a logarithmic function?

Back

3.

FLASHCARD QUESTION

Front

What is the base of a logarithm?

Back

4.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

5.

FLASHCARD QUESTION

Front

What does it mean to solve an inequality involving logarithms?

Back

Solving an inequality involving logarithms means finding the values of the variable that make the inequality true, often requiring the use of properties of logarithms.

6.

FLASHCARD QUESTION

Front

Back

This property states that the logarithm of a product is equal to the sum of the logarithms of the factors.

7.

FLASHCARD QUESTION

Front

Back

This property states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.

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