Growth/ Decay and Compound Interest

Front

What is compound interest?

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

How is compound interest calculated?

Back

Compound interest is calculated using the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is: y = a(1 - r)^t, where y is the remaining quantity, a is the initial quantity, r is the decay rate, and t is time.

Front

What is the half-life of a substance?

Back

The half-life is the time required for a quantity to reduce to half its initial value.

Front

If a printer costs $35,000 and depreciates at 5% per year, what is its value after 8 years?

Back

The value after 8 years is approximately $23,219.72.

Front

What does it mean for an interest rate to be compounded quarterly?

Back

Compounding quarterly means that the interest is calculated and added to the principal four times a year.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over time, while exponential decay occurs when a quantity decreases by a consistent percentage over time.

Front

How do you determine the remaining level of a substance after a certain time using half-life?

Back

You can determine the remaining level using the formula: y = a(1/2)^(t/h), where a is the initial amount, t is the total time, and h is the half-life.

Front

What is the formula for calculating the future value of an investment with compound interest?

Back

The future value of an investment with compound interest is calculated using the formula: A = P(1 + r/n)^(nt).

Front

What is the initial value of Prescription A in the given problem?

Back

The initial value of Prescription A is 1200 mg/L.