Exponential Functions Review

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for a quantity to decay exponentially?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often represented by the formula f(t) = f(0) * e^(-kt), where k is a positive constant.

Front

How do you calculate the future value of an investment with compound interest?

Back

The future value (FV) can be calculated using the formula FV = P(1 + r/n)^(nt), where 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

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = f(0) * e^(kt), where f(0) is the initial amount, k is a positive constant, and t is time.

Front

If a car depreciates by 10% each year, how do you express its value after 't' years?

Back

The value of the car after 't' years can be expressed as V(t) = V(0) * (1 - 0.10)^t, where V(0) is the initial value.

Front

What is the value of a car worth $20,000 after 3 years of 10% depreciation?

Back

After 3 years, the value of the car is approximately $14,580.

Front

How do you calculate the remaining amount of a radioactive substance after a certain time?

Back

The remaining amount can be calculated using the formula A(t) = A(0) * (1 - r)^t, where A(0) is the initial amount, r is the decay rate, and t is time.

Front

If a substance decays by 20% every hour, how much of a 500g sample remains after 4 hours?

Back

After 4 hours, approximately 204.8 grams of the substance remains.

Front

What is the equation for the value of land purchased for $30,000 increasing by 5% per year?

Back

Front

How do you find the balance in an account with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the amount in the account, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.