Exponential Growth and Decay Word Problems Practice

Front

What is exponential decay?

Back

Exponential decay refers to a decrease in a quantity by a consistent percentage over a period of time, resulting in a rapid decline.

Front

How do you calculate the population after a percentage decrease?

Back

Use the formula: P = P0 * (1 - r)^t, where P0 is the initial population, r is the rate of decrease (as a decimal), and t is the time in years.

Front

If a city has a population of 2,950,000 and decreases by 2.5% annually, what will be the population after 8 years?

Back

Population in 2008 = 2,950,000 * (1 - 0.025)^8 = 2,409,123.

Front

What is the formula for exponential growth?

Back

Exponential growth can be calculated using the formula: P = P0 * (1 + r)^t, where P0 is the initial amount, r is the growth rate (as a decimal), and t is the time in years.

Front

How do you find the value of a depreciating asset?

Back

Use the formula: V = V0 * (1 - r)^t, where V0 is the initial value, r is the depreciation rate (as a decimal), and t is the time in years.

Front

If a magazine has 98,000 subscribers and loses 10% each year, how many subscribers will it have in 10 years?

Back

Subscribers after 10 years = 98,000 * (1 - 0.10)^10 = 34,170.

Front

What does it mean for a car to depreciate at 11% per year?

Back

It means the car's value decreases by 11% of its current value each year.

Front

How do you calculate the future value of an asset that depreciates?

Back

Use the formula: Future Value = Initial Value * (1 - Depreciation Rate)^Number of Years.

Front

What is the significance of rounding in population and financial calculations?

Back

Rounding ensures that the results are presented as whole numbers for populations and to two decimal places for financial values.

Front

If a town produces 290,000 metric tons of CO2 and reduces emissions by 5% annually, what will be the emissions in 7 years?

Back

Emissions in 7 years = 290,000 * (1 - 0.05)^7 = 202,518.