How do you evaluate $$\text{log}_b(1)$$ ?

$$\text{log}_b(1) = 0$$ for any base $$b > 0$$ , because any number raised to the power of 0 equals 1.

What is the value of $$\text{log}_3igg(\frac{1}{3}igg)$$ ?

$$\text{log}_3igg(\frac{1}{3}igg) = -1$$ .

How do you determine if a function is exponential growth or decay from its equation?

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

What is the initial value in an exponential function?

The initial value in an exponential function is the value of the function when $$t = 0$$ , represented by $$a$$ in the function $$y = a(1 + r)^t$$ .

What is the formula for calculating the future value of an investment with compound interest?

The future value of an investment with compound interest is calculated using the formula $$A = P(1 + r/n)^{nt}$$ , where $$P$$ 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 the term 'base' refer to in logarithmic functions?

In logarithmic functions, the base is the number that is raised to a power to obtain a certain value. For example, in $$\text{log}_b(x)$$ , $$b$$ is the base.

What is the significance of the number 0 in logarithmic functions?

The logarithm of 0 is undefined because there is no exponent that can be applied to a positive base to yield 0.

How do you express a percentage increase in an exponential function?

A percentage increase of $$p%$$ can be expressed in an exponential function as $$y = a(1 + \frac{p}{100})^t$$ .

What is the value of $$\text{log}_4(4)$$ ?

$$\text{log}_4(4) = 1$$ , because 4 raised to the power of 1 equals 4.

Final Exam Review 3 - Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is the set of positive real numbers. Logarithms are undefined for zero and negative numbers.

3.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential growth?

Back

4.

FLASHCARD QUESTION

Front

What does it mean for a function to exhibit exponential decay?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the formula for exponential decay in terms of depreciation?

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between logarithms and exponents?

Back

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