Intro to Exponential Growth and 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 is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.

Front

What is the initial amount in an exponential function?

Back

The initial amount is the value of 'a' in the function f(x) = a * b^x, representing the starting quantity before any growth or decay.

Front

How do you identify exponential growth from a function?

Back

Exponential growth can be identified if the base 'b' in the function f(x) = a * b^x is greater than 1.

Front

How do you identify exponential decay from a function?

Back

Exponential decay can be identified if the base 'b' in the function f(x) = a * b^x is between 0 and 1.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is N(t) = N0 * e^(rt), where N0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is N(t) = N0 * e^(-rt), where N0 is the initial amount, r is the decay rate, and t is time.

Front

If a population doubles every week, how would you express its size after 't' weeks?

Back

The size after 't' weeks can be expressed as N(t) = N0 * 2^t, where N0 is the initial population.

Front

What does the term 'doubling time' refer to in exponential growth?

Back

Doubling time is the period it takes for a quantity to double in size during exponential growth.

Front

What is the decay constant in exponential decay?

Back

The decay constant is a positive number that describes the rate at which a quantity decreases in an exponential decay function.