Exponential Functions

Front

What is an exponential function?

Back

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

Front

What is the asymptote of the function y = 3^x?

Back

The asymptote of the function y = 3^x is y = 0.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify the equation of an exponential function from a graph?

Back

Look for the characteristic curve that rises or falls sharply, and identify key points to determine the base and vertical shifts.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

Front

What does the model P = A(1 + r)^t represent?

Back

This model represents exponential growth, where P is the future value, A is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the simplified form of (3x^4)(5x^3)?

Back

The simplified form is 15x^7.

Tags

CCSS.HSA.APR.A.1

Front

What is the general form of an exponential decay function?

Back

The general form 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 base of the exponential function y = 2^x?

Back

The base of the exponential function y = 2^x is 2.

Front

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

Back

To find the y-intercept, evaluate the function at x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is the value of y when x = 0 in the function y = 2^x?

Back

When x = 0, y = 2^0 = 1.

Tags

CCSS.HSF.LE.B.5