Exponential Equations - Table, Graphs, Equations

Front

What is an exponential equation?

Back

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 it is between 0 and 1, it represents exponential decay.

Front

How do you identify exponential growth in a table of values?

Back

Exponential growth can be identified in a table of values by observing that each value is multiplied by a constant factor (greater than 1) to get the next value.

Front

What is the general form of an exponential function?

Back

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant factor. For example, in linear growth, the difference between consecutive values is constant, whereas in exponential growth, the ratio of consecutive values is constant.

Front

How can you represent an exponential function graphically?

Back

An exponential function can be represented graphically with a curve that rises steeply (for growth) or falls sharply (for decay) as you move along the x-axis.

Front

What is the pattern in the sequence: 2, 6, 18, 54?

Back

The pattern is exponential growth, where each term is multiplied by 3 to get the next term (2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54).

Front

What does the y-intercept of an exponential function represent?

Back

Front

Back

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base in an exponential function affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 0 but less than 1) results in faster decay.