Exponential Growth & 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 the base (a positive real number), and 'x' is the exponent.

Front

What characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to an increase that accelerates over time.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when the decay rate of a value is proportional to its current value, leading to a decrease that slows over time.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x) where 0 < b < 1.

Front

In the function f(x) = 300(1.16)^x, what does '300' represent?

Back

'300' represents the initial amount or the value of the function when x = 0.

Front

In the function A = 1200(0.85)^x, what does '0.85' represent?

Back

'0.85' is the decay factor, indicating that the quantity decreases to 85% of its previous value.

Front

How do you identify exponential growth from a function?

Back

If the base 'b' in f(x) = a(b^x) is greater than 1, the function represents exponential growth.

Front

How do you identify exponential decay from a function?

Back

If the base 'b' in f(x) = a(b^x) is between 0 and 1, the function represents exponential decay.

Front

What is the decay factor in an exponential decay function?

Back

The decay factor is the base 'b' in the function f(x) = a(b^x) when 0 < b < 1.