A6 - Exponential Growth and Decay Word Problems

Front

What is exponential decay?

Back

Exponential decay is a process where a quantity decreases at a rate proportional to its current value, often modeled by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you model exponential growth?

Back

Exponential growth can be modeled by the equation 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 calculating the remaining amount after exponential decay?

Back

The formula is A = A0 * e^(-kt), where A0 is the initial amount, k is the decay constant, and t is time.

Front

If a population grows by 5% each year, what is the growth factor?

Back

The growth factor is 1.05.

Front

What does a decay rate of 50% mean in terms of value after one year?

Back

It means that after one year, the value will be half of the original value.

Front

How do you find the time it takes for an investment to double at a constant growth rate?

Back

You can use the Rule of 70: Time (years) = 70 / growth rate (percentage).

Front

What is the significance of the base 'e' in exponential functions?

Back

The base 'e' (approximately 2.718) is the natural base used in continuous growth or decay models.

Front

How do you calculate the future value of an investment with continuous compounding?

Back

Use the formula A = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current amount, leading to faster growth over time.

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.80.