4.2-4.4 Solving Exponential Word Problems

Front

What is the formula for compound interest when compounded semiannually?

Back

A = P(1 + r/n)^(nt), where A is the amount, P is the principal, 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 half-life of a substance?

Back

The half-life is the time required for half of the substance to decay or be eliminated.

Front

How do you calculate the remaining amount of a substance after a certain number of half-lives?

Back

Remaining amount = Initial amount * (1/2)^(number of half-lives).

Front

What is the formula for continuous compounding?

Back

A = Pe^(rt), where A is the amount, P is the principal, r is the annual interest rate, t is the time in years, and e is Euler's number (approximately 2.71828).

Front

What does it mean for a quantity to decrease by a certain percentage each year?

Back

It means that each year, the quantity is multiplied by (1 - percentage decrease). For example, a 30% decrease means multiplying by 0.7.

Front

Write the exponential decay equation for a quantity that starts at 5000 and decreases by 30% each year.

Back

y = 5000(0.7)^x, where y is the quantity after x years.

Front

What is the effective interest rate for an account compounded monthly?

Back

Effective interest rate = (1 + r/n)^(nt) - 1, where r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years.

Front

How do you find the total amount paid on a loan with compound interest?

Back

Total amount paid = Principal + Interest, where Interest can be calculated using the compound interest formula.

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 that has been added to it.

Front

If a bacteria culture starts with 5000 cells and dies by 30% each year, how many cells are left after 3 years?

Back

y = 5000(0.7)^3 = 5000 * 0.343 = 1715 cells.