What is the formula for exponential growth?

The formula for exponential growth is $$y = y_0 e^{rt}$$ , where $$y_0$$ is the initial amount, $$r$$ is the growth rate, and $$t$$ is time.

What is the difference between exponential growth and decay?

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when it decreases at a rate proportional to its current value.

How do you condense logarithmic expressions?

To condense logarithmic expressions, use the properties of logarithms, such as $$a \text{log}_b(c) = \text{log}_b(c^a)$$ .

What is the relationship between exponential and logarithmic functions?

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

What is the formula for the population growth model?

The population growth model can be expressed as $$P(t) = P_0 e^{rt}$$ , where $$P_0$$ is the initial population, $$r$$ is the growth rate, and $$t$$ is time.

How do you graph an exponential function?

To graph an exponential function, identify the y-intercept, determine the growth or decay rate, and plot points for various values of $$x$$ .

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

The number $$e$$ is the base of natural logarithms and is significant in calculus, particularly in growth and decay problems, as it represents continuous growth.

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 $$k$$ .

Unit 6 Review: Exponential and Logarithmic Functions 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 the base of a logarithm?

Back

3.

FLASHCARD QUESTION

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides or rewrite the equation in a form that allows you to isolate the variable.

4.

FLASHCARD QUESTION

Front

What is the inverse of an exponential function?

Back

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