Exponential Growth and Decay Word Problems

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate. It can be modeled by the formula: $$y = a(1 + r)^t$$ where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline. It can be modeled by the formula: $$y = a(1 - r)^t$$ where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

'a' represents the initial amount or the starting value before any growth occurs.

'r' represents the growth rate in exponential growth and the decay rate in exponential decay, expressed as a decimal.

To calculate the final amount after exponential growth, use the formula: $$y = a(1 + r)^t$$ where 'a' is the initial amount, 'r' is the growth rate, and 't' is the time in years.

To calculate the final amount after exponential decay, use the formula: $$y = a(1 - r)^t$$ where 'a' is the initial amount, 'r' is the decay rate, and 't' is the time in years.

The decay rate is 0.05.

The formula is: $$y = a(1 - r)^t$$ where 'y' is the final population, 'a' is the initial population, 'r' is the decay rate, and 't' is the number of years.

Using the formula $$y = 10000(1 - 0.05)^{20}$$ , the population will be approximately 3,585.

'y' stands for the final amount after growth has occurred.