How do you solve the equation $$5^{a + 2} = \frac{1}{125}$$ ?

Convert $$\frac{1}{125}$$ to an exponential form: $$125 = 5^3$$ , so $$\frac{1}{125} = 5^{-3}$$ . Therefore, set the exponents equal: $$a + 2 = -3$$ , leading to $$a = -5$$ .

How do you solve $$3^3 = 3^{4x + 2}$$ ?

Since the bases are the same, set the exponents equal: $$3 = 4x + 2$$ . Solving gives $$x = \frac{1}{4}$$ .

What is the significance of the base in an exponential function?

The base determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

What is the value of $$x$$ in the equation $$2^x = 16$$ ?

Convert 16 to an exponential form: $$16 = 2^4$$ . Therefore, set the exponents equal: $$x = 4$$ .

How do you graph an exponential function?

To graph an exponential function, plot points for various values of $$x$$ , noting that the function approaches the x-axis but never touches it (asymptote).

What is an asymptote in the context of exponential functions?

An asymptote is a line that a graph approaches but never touches. For exponential functions, the x-axis (y=0) is a horizontal asymptote.

What is the solution to the equation $$2^{x-1} = 8$$ ?

Convert 8 to an exponential form: $$8 = 2^3$$ . Set the exponents equal: $$x - 1 = 3$$ , leading to $$x = 4$$ .

What is the relationship between exponential functions and logarithms?

Logarithms are the inverse operations of exponential functions. For example, if $$y = b^x$$ , then $$x = log_b(y)$$ .

How do you identify the y-intercept of an exponential function?

The y-intercept occurs when $$x = 0$$ . For $$y = ab^x$$ , the y-intercept is $$y = a$$ .

What is the solution to the equation $$5^{a + 2} = 1/125$$ ?

Convert $$1/125$$ to exponential form: $$1/125 = 5^{-3}$$ . Set the exponents equal: $$a + 2 = -3$$ , leading to $$a = -5$$ .

Exponential Equations Review Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential equation?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit growth?

Back

A function exhibits growth if its value increases as the input increases. In exponential functions, if the base is greater than 1, it represents growth.

4.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit decay?

Back

A function exhibits decay if its value decreases as the input increases. In exponential functions, if the base is between 0 and 1, it represents decay.

5.

FLASHCARD QUESTION

Front

Back

Since the base (1.35) is greater than 1, the function is a growth function.

6.

FLASHCARD QUESTION

Front

What is the general form of an exponential function?

Back

7.

FLASHCARD QUESTION

Front

Back

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