Exponential Growth or Decay?

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 a positive real number, and 'x' is the exponent.

Front

What characterizes exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal time intervals, leading to a rapid decrease.

Front

What is the base in an exponential function?

Back

The base in an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

If b > 1 in f(x) = a * b^x, what type of function is it?

Back

If b > 1, the function represents exponential growth.

Front

If 0 < b < 1 in f(x) = a * b^x, what type of function is it?

Back

If 0 < b < 1, the function represents exponential decay.

Front

What is the formula for calculating exponential growth?

Back

The formula for exponential growth is A = A0 * e^(rt), where A0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for calculating exponential decay?

Back

The formula for exponential decay is A = A0 * e^(-rt), where A0 is the initial amount, r is the decay rate, and t is time.

Front

How does the graph of an exponential growth function behave?

Back

The graph of an exponential growth function rises steeply as x increases, approaching infinity.

Front

How does the graph of an exponential decay function behave?

Back

The graph of an exponential decay function decreases rapidly and approaches zero as x increases.