Exponential Growth and Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, represented by the equation A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time, represented by the equation A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Front

Identify the initial value in the function: f(x) = 500(1.05)^x.

Back

The initial value is 500.

Front

Classify the model: A = 200(0.9)^t. Is it Growth or Decay?

Back

Decay.

Front

What is the formula for continuous exponential growth?

Back

The formula is A = Pe^(rt), where e is the base of the natural logarithm, P is the initial amount, r is the growth rate, and t is time.

Front

Evaluate the expression f(x) = 150(0.75)^x for f(2).

Back

f(2) = 150(0.75)^2 = 84.375.

Front

What is the equation for the exponential function that models a population doubling every 3 years?

Back

The equation is P(t) = P_0(2)^(t/3), where P_0 is the initial population.

Front

What does a negative exponent in an exponential function indicate?

Back

A negative exponent indicates a decay process, meaning the quantity is decreasing.

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.8.