5.2 Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

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

Front

How do you calculate future value in exponential growth?

Back

Future Value = Present Value * (1 + growth rate)^number of periods.

Front

How do you calculate future value in exponential decay?

Back

Future Value = Present Value * (1 - decay rate)^number of periods.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.

Front

If a population doubles every 2 days, how do you express this mathematically?

Back

Population(t) = Initial Population * 2^(t/2), where t is the time in days.

Front

What does a 15% annual increase mean in terms of growth?

Back

It means that each year, the quantity increases by 15% of its value from the previous year.

Front

What does a 5% annual decrease mean in terms of decay?

Back

It means that each year, the quantity decreases by 5% of its value from the previous year.

Front

How do you round numbers in exponential problems?

Back

Round to the nearest whole number if necessary, following standard rounding rules.

Front

What is the significance of the base in exponential functions?

Back

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