Comparing 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 does the base 'b' in an exponential function represent?

Back

The base 'b' in an exponential function determines the growth or decay rate of the function. If b > 1, the function grows; if 0 < b < 1, the function decays.

Front

How do you identify the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function y = a(b^x). It indicates how much the function increases for each unit increase in x.

Front

What is the difference between growth and decay in exponential functions?

Back

Growth occurs when the base 'b' is greater than 1, leading to an increase in y as x increases. Decay occurs when 0 < b < 1, leading to a decrease in y as x increases.

Front

How can you compare the growth rates of two exponential functions?

Back

To compare growth rates, look at the bases of the functions. The function with the larger base grows faster.

Front

What is the effect of changing the initial value 'a' in an exponential function?

Back

Changing the initial value 'a' affects the starting point of the function on the y-axis but does not affect the growth or decay rate.

Front

If y = 2(3^x), what is the growth factor?

Back

The growth factor is 3.

Front

Which function grows faster: y = 2^x or y = 3^x?

Back

y = 3^x grows faster than y = 2^x.

Front

If y = (1/2)^x and y = (1/4)^x, which function decays faster?

Back

y = (1/4)^x decays faster than y = (1/2)^x.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(b^x), where 0 < b < 1.