5.2 Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in 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 process where a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

How do you calculate the future value of an investment with compound interest?

Back

Future Value = Principal × (1 + r/n)^(nt), where r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the formula for population growth?

Back

Population at time t = P0 × (1 + r)^t, where P0 is the initial population, r is the growth rate, and t is time.

Front

What is the formula for population decay?

Back

Population at time t = P0 × (1 - r)^t, where P0 is the initial population, r is the decay rate, and t is time.

Front

If a population doubles every 2 days, how can you express this mathematically?

Back

If P0 is the initial population, then after t days, the population can be expressed as P(t) = P0 × 2^(t/2).

Front

What is the effective interest rate?

Back

The effective interest rate is the actual interest rate an investor earns or pays after accounting for compounding over a given period.

Front

How do you find the time it takes for a population to reach a certain size with exponential growth?

Back

Use the formula: t = (log(final population/P0)) / (log(1 + r)).

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest earned.

Front

How do you calculate the amount of interest earned on an investment?

Back

Interest Earned = Future Value - Principal.