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 base 'b' in an exponential function represent?

Back

The base 'b' represents the growth factor of the function. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent.

Front

What is the y-intercept of an exponential function f(x) = a * b^x?

Back

The y-intercept is the value of the function when x = 0, which is f(0) = a.

Front

How do you identify an exponential function from a given equation?

Back

An exponential function can be identified if the variable is in the exponent, such as in the form y = a * b^x.

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 percentage, leading to faster growth over time.

Front

If a population doubles every year, what type of function describes this growth?

Back

This growth is described by an exponential function.

Front

What does the 'a' represent in the exponential function f(x) = a * b^x?

Back

The 'a' represents the initial value or y-intercept of the function.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'k' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay rate, and 't' is time.