Exponential Growth and Decay word problems

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at a rate that accelerates over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease in a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

How do you calculate the future value of an investment with exponential growth?

Back

The future value can be calculated using the formula: FV = P(1 + r)^t, where P is the principal amount, r is the growth rate, and t is the time in years.

Front

What is the decay factor in exponential decay?

Back

The decay factor is the percentage of the quantity that remains after each time period, expressed as a decimal. It is calculated as 1 - decay rate.

Front

How do you determine the initial value in an exponential decay problem?

Back

The initial value is the starting amount before any decay occurs, often denoted as 'P' in the decay formula.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is: y = P(1 - r)^t, where P is the initial amount, r is the decay rate, and t is the time.

Front

What does a decay rate of 20% per hour mean?

Back

A decay rate of 20% per hour means that 20% of the substance is lost every hour, leaving 80% remaining after each hour.

Front

How can you model the value of a depreciating asset?

Back

The value of a depreciating asset can be modeled using the formula: V = V0 * (1 - d)^t, where V0 is the initial value, d is the decay rate, and t is the time.

Front

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

Back

The base in an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you find the value of an investment after a certain number of years with compound interest?

Back

You can find the value using the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.