Exponential Growth and Decay Applications

Front

What is exponential growth?

Back

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

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

How do you calculate the future value of an investment with compound interest?

Back

Future Value = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the formula for calculating depreciation?

Back

Depreciation can be calculated using the formula: Value = Initial Value * (1 - rate)^t, where rate is the depreciation rate and t is the time in years.

Front

What is the decay factor in exponential decay?

Back

The decay factor is calculated as (1 - rate). For example, if the rate is 8%, the decay factor is 0.92.

Front

What does it mean for an investment to be compounded semiannually?

Back

Compounding semiannually means that interest is calculated and added to the principal twice a year.

Front

How do you determine if a model represents exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

Front

What is the significance of the interest rate in compound interest calculations?

Back

The interest rate determines how much interest is earned on the principal over time; a higher rate results in more interest accrued.

Front

How do you find the total amount paid on a loan with compound interest?

Back

Total Amount = Principal + Interest, where Interest can be calculated using the compound interest formula.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has been added.