Unit 5 - 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 initial value represent in an exponential function?

Back

The initial value is the value of the function when x = 0, representing the starting amount before any growth or decay occurs.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b)^x when b > 1, indicating how much the quantity increases.

Front

What is the decay factor in an exponential function?

Back

The decay factor is the base 'b' in the function f(x) = a(b)^x when 0 < b < 1, indicating how much the quantity decreases.

Front

How can you determine if an exponential function represents growth or decay?

Back

If the base 'b' is greater than 1, the function represents exponential growth. If 'b' is between 0 and 1, it represents exponential decay.

Front

In the function j(x) = 8(1.1)^x, what does the number 8 represent?

Back

The number 8 represents the initial value of the function.

Front

In the function E(x) = 236(0.94)^x, what does the base 0.94 indicate?

Back

The base 0.94 indicates that the population is decreasing by 6% each time period.

Front

What does the function p(x) = 15(0.7)^x represent?

Back

The function represents exponential decay, as the base 0.7 is less than 1.

Front

What does the function g(x) = 7(1.2)^x represent?

Back

The function represents exponential growth, as the base 1.2 is greater than 1.

Front

What is the significance of the exponent in an exponential function?

Back

The exponent indicates the number of time periods that have passed, affecting the growth or decay of the function.