Exponential Growth and Decay

Front

What is the general form of an exponential growth function?

Back

A = A_0(1 + r)^t, where A_0 is the initial amount, r is the growth rate, and t is time.

Front

What is the general form of an exponential decay function?

Back

A = A_0(1 - r)^t, where A_0 is the initial amount, r is the decay rate, and t is time.

Front

How do you determine if a function 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 relationship between growth rate and growth factor?

Back

The growth factor is calculated as 1 + growth rate (in decimal form). For example, a growth rate of 44% corresponds to a growth factor of 1.44.

Front

What is the relationship between decay rate and decay factor?

Back

The decay factor is calculated as 1 - decay rate (in decimal form). For example, a decay rate of 20% corresponds to a decay factor of 0.8.

Front

If a population doubles every 5 years, what is the growth factor per year?

Back

The growth factor per year can be calculated using the formula: growth factor = 2^(1/5) ≈ 1.1487.

Front

What is the formula to calculate the time it takes for an investment to double at a constant growth rate?

Back

The Rule of 70: Time (in years) = 70 / growth rate (in percentage).

Front

How do you convert a percentage growth rate to a decimal for calculations?

Back

Divide the percentage by 100. For example, a growth rate of 44% becomes 0.44.

Front

What is the decay factor if the decay rate is 15%?

Back

The decay factor is 1 - 0.15 = 0.85.

Front

Write the exponential decay equation for a substance that decreases by 25% each year starting with 100 grams.

Back

y = 100(0.75)^x.