Q2: Pre-AP Algebra 2 Retake on Flashcard#1 for Unit 1: L1.4-L1.5

Front

What is the general form of an exponential growth function?

Back

An exponential growth function can be expressed as A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is the time period.

Front

What is the general form of an exponential decay function?

Back

An exponential decay function can be expressed as A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is the time period.

Front

How do you determine if a function represents exponential 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 formula to calculate 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, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

How do you calculate the future value of an investment compounded monthly?

Back

To calculate the future value of an investment compounded monthly, use the formula A = P(1 + r/12)^(12t), where P is the principal, r is the annual interest rate, and t is the number of years.

Front

What is the difference between annual, monthly, and daily compounding?

Back

Annual compounding calculates interest once a year, monthly compounding calculates interest 12 times a year, and daily compounding calculates interest 365 times a year, leading to different total amounts due to the frequency of interest application.

Front

How do you predict future tuition costs using an exponential function?

Back

To predict future tuition costs, substitute the number of years since the college opened into the function T = 12,000(1.03)^x, where x is the number of years since the college opened.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function indicates the growth or decay factor; a base greater than 1 indicates growth, while a base less than 1 indicates decay.

Front

How do you calculate the total amount in a savings account after a certain number of years with a fixed interest rate?

Back

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

Front

What is the impact of compounding frequency on investment growth?

Back

The more frequently interest is compounded, the more interest will be earned on the investment, leading to a higher total amount.