(03/08) 4th Pd Solving Exp/Log Word Problems Flashcard

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical expression that describes a quantity increasing at a constant percentage rate over time, typically represented as y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

How do you model a situation where a value increases by a percentage each year?

Back

You can model it using the formula y = a(1 + r)^t, where 'a' is the original value, 'r' is the growth rate (as a decimal), and 't' is the number of years.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount (initial investment), 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 does it mean for a value to decay?

Back

Decay refers to a decrease in value over time, often modeled by an exponential decay function, which can be expressed as y = a(1 - r)^t, where 'a' is the initial value, 'r' is the decay rate, and 't' is time.

Front

How do you determine if an equation represents growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the value of a $20,000 car after 3 years if it depreciates at 12% per year?

Back

The value after 3 years is approximately $13,629.44.

Front

If a computer worth $2100 decreases by 50% annually, what is its value after 2 years?

Back

The value after 2 years is $525.

Front

How do you calculate the balance of an investment compounded semi-annually?

Back

Use the formula A = P(1 + r/2)^(2t), where P is the principal, r is the annual interest rate, and t is the number of years.

Front

What is the result of $300 invested at 6.5% for 4 years compounded semi-annually?

Back

The balance is approximately $387.47.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over time, while exponential growth increases by a constant percentage, leading to faster growth as time progresses.