Exponential Characteristics

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase that can be represented by the function y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, resulting in a rapid decrease that can be represented by the function 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 general form of an exponential function?

Back

The general form of an exponential function is y = ab^x, where a is a constant, b is the base (b > 0), and x is the exponent.

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay factor. 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

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

Back

The y-intercept of an exponential function can be found by evaluating the function at x = 0. For y = ab^x, the y-intercept is (0, a).

Tags

CCSS.HSF-IF.C.7E

Front

What is the left end behavior of an exponential function with a positive base?

Back

For an exponential function with a positive base, as x approaches negative infinity (x → -∞), y approaches 0 (y → 0).

Tags

CCSS.HSF-IF.C.7E

Front

What is the right end behavior of an exponential growth function?

Back

For an exponential growth function, as x approaches positive infinity (x → ∞), y approaches positive infinity (y → ∞).

Tags

CCSS.HSF-IF.C.7E

Front

What is the right end behavior of an exponential decay function?

Back

For an exponential decay function, as x approaches positive infinity (x → ∞), y approaches 0 (y → 0).

Tags

CCSS.HSF-IF.C.7E

Front

How can you express repeated multiplication using exponents?

Back

Repeated multiplication can be expressed using exponents by writing the base multiplied by itself a certain number of times as base^n, where n is the number of times the base is multiplied.

Tags

CCSS.6.EE.A.1

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0, providing insight into the starting point of the growth or decay process.

Tags

CCSS.HSF-IF.C.7E