Flashcard # 5

Front

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

Back

Future Value = P(1 + r)^t, where P is the principal amount, r is the annual interest rate, and t is the number of years.

Front

Define exponential growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to a rapid increase over time.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

If a quantity doubles every year, what type of growth is it experiencing?

Back

Exponential growth.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300.

Front

How do you calculate the depreciation of an asset?

Back

Depreciation can be calculated using the formula: Value = Initial Value * (1 - rate)^t, where rate is the annual depreciation rate and t is the number of years.

Front

What is the value of a car that depreciates at 12% annually if it was bought for $13,000 after 3 years?

Back

Value = 13000 * (1 - 0.12)^3 = $9,000.56.

Front

What does a 5% annual increase in value mean?

Back

It means that each year, the value increases by 5% of its previous year's value.

Front

How much will Jack have after investing $600 at a 5% interest rate for 5 years?

Back

Jack will have $765.77.

Front

What is the formula for calculating the value of an asset after t years with a constant rate of decay?

Back

Value = Initial Value * (1 - decay rate)^t.