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

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

How do you calculate the amount after a certain number of years with compound interest?

Back

Use the compound interest formula: A = P(1 + r/n)^(nt). Substitute the values for P, r, n, and t to find A.

Front

What does it mean for a quantity to decrease by a percentage each year?

Back

It means that each year, the quantity is reduced by that percentage of its current value, leading to a smaller amount each subsequent year.

Front

How do you find the remaining quantity after a percentage decrease over multiple years?

Back

Use the formula: Remaining Quantity = Initial Quantity * (1 - rate)^number of years.

Front

What is the significance of rounding in exponential problems?

Back

Rounding is important to provide a practical answer, especially in financial and real-world contexts where exact values may not be feasible.

Front

If a quantity decreases by 10% each year, what is the multiplier for each year?

Back

The multiplier is 0.90 (1 - 0.10). This means you multiply the current quantity by 0.90 each year.

Front

What is the effect of compounding frequency on compound interest?

Back

The more frequently interest is compounded, the more interest will be earned, as interest is calculated on previously earned interest.

Front

How do you calculate the interest earned in a savings account?

Back

Subtract the principal from the total amount after the specified time using the compound interest formula.