Exponential Growth

Front

What is exponential growth?

Back

Exponential growth is a process where the quantity increases by a consistent percentage over a specific period of time, leading to rapid growth as time progresses.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate (as a decimal), and 't' is the time period.

Front

If a population of 4,000 mosquitoes grows at a rate of 25% per month, how do you calculate the population after 4 months?

Back

Use the formula: y = 4000(1 + 0.25)^4. Calculate to find y.

Front

What does the initial value represent in an exponential function?

Back

The initial value represents the starting amount before any growth occurs.

Front

How do you convert a percentage growth rate to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 25% becomes 0.25.

Front

What is the significance of the exponent in an exponential function?

Back

The exponent indicates the number of time periods the growth occurs, affecting the final amount significantly.

Front

How do you write an exponential growth function for a value increasing by 9% each year starting at $1400?

Back

The function is y = 1400(1.09)^x.

Front

What is the value of a home worth today if it was purchased for $160,000 and increases by 5% per year for 20 years?

Back

The value today is approximately $424,527.63.

Front

What does the term 'growth rate' refer to in exponential growth?

Back

The growth rate is the percentage at which a quantity increases over a specific time period.

Front

How do you determine the final amount in an exponential growth scenario?

Back

Substitute the values into the exponential growth formula and calculate.