How do you solve the equation $$b^x = b^y$$ ?

If $$b^x = b^y$$ , then $$x = y$$ , provided that $$b > 0$$ and @@b eq 1@@.

What is the property of exponents that states $$(b^m)^n = b^{m \times n}$$ ?

This property is known as the Power of a Power Property.

How do you solve the equation $$9^{8-x} = 27^{x-3}$$ ?

Convert both sides to the same base: $$9 = 3^2$$ and $$27 = 3^3$$ , leading to $$(3^2)^{8-x} = (3^3)^{x-3}$$ , which simplifies to $$x = 5$$ .

What is the general form of an exponential growth function?

The general form is $$f(t) = a(1 + r)^t$$ , where $$a$$ is the initial amount, $$r$$ is the growth rate, and $$t$$ is time.

What is the general form of an exponential decay function?

The general form is $$f(t) = a(1 - r)^t$$ , where $$a$$ is the initial amount, $$r$$ is the decay rate, and $$t$$ is time.

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

The constant $$e$$ (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models.

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse functions; if $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

What is the domain and range of an exponential function?

The domain of an exponential function is all real numbers ( $$(-\text{∞}, \text{∞})$$ ), and the range is positive real numbers (0, $$\text{∞}$$ ).

Exponential Functions Flashcard

Student preview

16 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the base of an exponential function?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What is the y-intercept of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

4.

FLASHCARD QUESTION

Front

What is the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept because it never crosses the x-axis; it approaches zero but never reaches it.

Tags

CCSS.HSF-IF.C.7E

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

This property is known as the Product of Powers Property.

Tags

CCSS.8.EE.A.1

7.

FLASHCARD QUESTION

Front

Back

This property is known as the Quotient of Powers Property.

Tags

CCSS.8.EE.A.1

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