Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What are the characteristics of the graph of an exponential function?

Back

The graph of an exponential function is a smooth curve that either increases or decreases rapidly. It has a horizontal asymptote, typically the x-axis, and does not intersect it.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify the base of an exponential function from its equation?

Back

In the equation f(x) = a * b^x, the base 'b' is the number that is raised to the power of 'x'. It is the coefficient of the exponential term.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value as 'x' increases.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'e' is Euler's number (approximately 2.718), 'k' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'e' is Euler's number, 'k' is the decay rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

How do you convert an exponential function to logarithmic form?

Back

To convert an exponential function of the form b^y = x to logarithmic form, you write it as log_b(x) = y.

Tags

CCSS.HSF.BF.B.5

Front

What is the inverse of an exponential function?

Back

The inverse of an exponential function is a logarithmic function. If f(x) = b^x, then its inverse is f^(-1)(x) = log_b(x).

Tags

CCSS.HSF-BF.B.4A

Front

What is the domain and range of an exponential function?

Back

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

Front

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

Back

The y-intercept of an exponential function f(x) = a * b^x is found by evaluating f(0), which equals a, since b^0 = 1.

Tags

CCSS.HSF-IF.C.7E