Exponential Growth, Decay, and Compound Interest

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 an increasing rate 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

Define compound interest.

Back

Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods, leading to exponential growth of the investment.

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, 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 continuous compounding?

Back

A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

If a car's value increases by 10% each year, how do you express this mathematically?

Back

Value after t years = Initial Value * (1 + 0.10)^t.

Front

How do you calculate the expected number of voters after a percentage decrease?

Back

Expected Voters = Current Voters * (1 - decrease rate)^t.

Front

What is the significance of rounding in financial calculations?

Back

Rounding is important in financial calculations to ensure that values are presented in a practical format, often to the nearest cent or whole number.

Front

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

Back

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

Front

What is the impact of a higher interest rate on compound interest?

Back

A higher interest rate increases the amount of interest earned or paid, leading to greater growth or cost over time.