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 a consistent percentage rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a consistent percentage decrease over time.

Front

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

Back

Future Value = Present Value × (1 + growth rate)^number of years.

Front

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

Back

Future Value = Present Value × (1 - decay rate)^number of years.

Front

What is the formula for exponential growth?

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a car costs $18,000 and increases by 5% each year, what will it cost in 7 years?

Back

$25,327.81.

Front

If a sculpture is worth $1200 and increases by 8% each year, what will it be worth in 25 years?

Back

$8,218.17.

Front

What is the initial amount in the function y = 15(1.35)^x?

Back

The initial amount is $15.

Front

If a population decreases by 1.5% per year from 120,000, what will it be in 40 years?

Back

65,559.