The Natural Base e

Front

What is the formula for continuous compound interest?

Back

Front

How do you calculate the amount of money in an account after continuous compounding?

Back

Front

What does the variable 'e' represent in the context of continuous compounding?

Back

The variable 'e' is a mathematical constant approximately equal to 2.71828. It is the base of the natural logarithm and is used in continuous compounding to model exponential growth.

Front

If you deposit $5,000 at an interest rate of 3% compounded continuously, how much will you have after 8 years?

Back

Front

What is radioactive decay?

Back

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process results in the transformation of the original element into a different element or isotope.

Front

How do you determine the initial amount of a radioactive substance from a decay graph?

Back

The initial amount of a radioactive substance can be determined by locating the y-intercept of the decay graph, which represents the quantity of the substance at time zero.

Front

What is half-life in the context of radioactive decay?

Back

Half-life is the time required for half of the radioactive atoms in a sample to decay. It is a constant for each radioactive isotope.

Front

If Sodium-22 has a half-life of 2.6 years, how much of a 15 mg sample remains after 5.2 years?

Back

After 5.2 years (which is two half-lives), the remaining amount is: 15 mg / 2^2 = 15 mg / 4 = 3.75 mg.

Front

What is the relationship between half-life and decay rate?

Back

The decay rate is inversely related to the half-life; a shorter half-life indicates a faster decay rate, while a longer half-life indicates a slower decay rate.

Front

How can you express the remaining amount of a radioactive substance after a certain time?

Back