Exponential Functions

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 does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the initial amount in an exponential function?

Back

The initial amount, denoted as 'a' in the function f(x) = a(b^x), represents the value of the function when x = 0.

Tags

CCSS.HSF.LE.B.5

Front

How do you solve exponential equations?

Back

To solve exponential equations, you can use properties of exponents, take logarithms, or rewrite the equation in a form that allows for comparison of bases.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the range of an exponential function?

Back

The range of an exponential function f(x) = a(b^x) is (0, ∞) if a > 0, and (-∞, 0) if a < 0.

Tags

CCSS.HSF-IF.C.7E

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'.

Tags

CCSS.HSF-IF.C.7E

Front

What is the relationship between exponential functions and logarithms?

Back

Exponential functions and logarithms are inverse functions. If y = b^x, then x = log_b(y).

Tags

CCSS.HSF.BF.B.5

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you express a number in exponential form?

Back

To express a number in exponential form, identify the base and the exponent that represent the number, such as 8 = 2^3.

Tags

CCSS.6.EE.A.1