How do you calculate the future value of an investment using exponential growth?

Use the formula $$V = P(1 + r)^t$$ , where 'P' is the principal amount, 'r' is the rate of interest, and 't' is the time in years.

What is the formula for continuous exponential growth?

The formula for continuous exponential growth is $$N(t) = N_0 e^{rt}$$ , where 'N_0' is the initial amount, 'e' is Euler's number, 'r' is the growth rate, and 't' is time.

What is the effect of a negative growth rate in an exponential function?

A negative growth rate indicates exponential decay, meaning the quantity decreases over time.

How do you determine the half-life of a substance in exponential decay?

The half-life is the time required for a quantity to reduce to half its initial value, calculated using the formula $$t_{1/2} = \frac{\text{ln}(2)}{r}$$ .

What is the relationship between exponential functions and logarithms?

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

How can 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 the significance of the y-intercept in an exponential function?

The y-intercept indicates the initial value of the function when x = 0, which is crucial for understanding the function's behavior.

How do you solve for 'x' in an exponential equation?

To solve for 'x' in an exponential equation, take the logarithm of both sides, using the appropriate base.

Exponential Functions 2 Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

5.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

6.

FLASHCARD QUESTION

Front

If a quantity doubles every year, what is the growth factor?

Back

The growth factor is 2, meaning the base 'b' in the exponential function is 2.

7.

FLASHCARD QUESTION

Front

Back

The 'a' represents the initial value or the y-intercept of the function.

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