Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease.

Front

Write the general 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

Write the general 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

In the formula y = a(1 + r)^t, what does 'r' represent?

Back

'r' represents the growth rate expressed as a decimal.

Front

In the formula y = a(1 - r)^t, what does 'r' represent?

Back

'r' represents the decay rate expressed as a decimal.

Front

If a population of 1000 increases by 5% each year, what will be the population after 3 years?

Back

Population after 3 years = 1000(1 + 0.05)^3 = 1157.63.

Front

If a car's value is $20,000 and it depreciates at 15% per year, what will its value be after 2 years?

Back

Value after 2 years = 20000(1 - 0.15)^2 = $14,450.

Front

What does the variable 'a' represent in the exponential growth/decay formulas?

Back

'a' represents the initial amount or starting value before growth or decay.

Front

How do you determine if a situation involves growth or decay?

Back

If the rate is positive, it is growth; if the rate is negative, it is decay.