Half Life & Doubling Time

Front

What is Half-Life?

Back

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in the context of radioactive decay.

Front

What is Doubling Time?

Back

Doubling time is the period of time required for a quantity to double in size or value, often used in population growth and investment contexts.

Front

How do you calculate Doubling Time using the Rule of 70?

Back

Doubling Time (in years) = 70 / growth rate (as a percentage). For example, if the growth rate is 7%, Doubling Time = 70 / 7 = 10 years.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, 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

If an investment of $1000 grows to $2000, what is the doubling time if it took 5 years?

Back

The doubling time is 5 years.

Front

What is the depreciation formula for an asset?

Back

Value = Initial Value * (1 - depreciation rate)^t, where t is the number of years.

Front

If a car depreciates by 20% each year, what is its value after 3 years if it started at $25,000?

Back

Value = 25000 * (1 - 0.20)^3 = $12,800.

Front

What is the significance of the 28% depreciation rate in the context of automobiles?

Back

A 28% depreciation rate means that the car loses 28% of its value each year, affecting its resale value.

Front

How do you find the half-life of a depreciating asset?

Back

The half-life can be calculated using the formula: Half-life = ln(0.5) / ln(1 - depreciation rate).

Front

What is the growth rate if a plant grows from 3 cm to 6 cm in 10 days?

Back

Growth rate = (final height - initial height) / initial height * (1 / time) = (6 - 3) / 3 * (1 / 10) = 0.1 or 10%.