What is the Quotient of Powers Property?

The Quotient of Powers Property states that $$\frac{a^m}{a^n} = a^{m-n}$$ .

What is the formula for compound interest?

The formula for compound interest is $$A = P(1 + \frac{r}{n})^{nt}$$ , 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 is the Exponential Growth Formula?

The Exponential Growth Formula is $$N(t) = N_0 e^{rt}$$ , where $$N(t)$$ is the amount at time $$t$$ , $$N_0$$ is the initial amount, $$r$$ is the growth rate, and $$e$$ is the base of the natural logarithm.

What is the Exponential Decay Formula?

The Exponential Decay Formula is $$N(t) = N_0 e^{-rt}$$ , where $$N(t)$$ is the amount at time $$t$$ , $$N_0$$ is the initial amount, and $$r$$ is the decay rate.

What is the definition of a logarithm?

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base $$b$$ be raised, to produce a number $$x$$ ? It is written as $$\text{log}_b(x) = y$$ , which means $$b^y = x$$ .

What is the change of base formula for logarithms?

The change of base formula states that $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any positive base $$k$$ .

What is the relationship between exponential and logarithmic functions?

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

Exponential Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define an exponential equation.

Back

2.

FLASHCARD QUESTION

Front

What is the general form of an exponential function?

Back

3.

FLASHCARD QUESTION

Front

Back

x = 1.

4.

FLASHCARD QUESTION

Front

What is the base of an exponential function?

Back

5.

FLASHCARD QUESTION

Front

Back

x = 12.

6.

FLASHCARD QUESTION

Front

Back

This property is known as the Product of Powers Property.

7.

FLASHCARD QUESTION

Front

Back

x = 0.

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