IM Algebra Unit 5 Review

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, including interest. P is the principal amount (the initial amount of money), 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 the money is invested or borrowed.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (f(x)) also increases. This means that for any two points x1 and x2 where x1 < x2, f(x1) < f(x2).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (f(x)) decreases. This means that for any two points x1 and x2 where x1 < x2, f(x1) > f(x2).

Front

What is the value of c(0) in the function c(x) = 250(1 + 0.6)^x?

Back

c(0) = 250(1 + 0.6)^0 = 250(1) = 250. This represents the initial value of the function when x = 0.

Front

How do you calculate the future value of an investment with a growth rate?

Back

To calculate the future value of an investment with a growth rate, use the formula: Future Value = Present Value * (1 + growth rate)^number of periods.

Front

What is the initial cost represented by c(x) = 110(1.06)^x in 2015?

Back

The initial cost in 2015 is c(0) = 110(1.06)^0 = 110. This is the cost at the start of the time period.

Front

If a quantity increases by 20% each month, what is the growth factor?

Back

The growth factor for a 20% increase is 1 + 0.20 = 1.20.

Front

How do you find the total amount sold after multiple periods of growth?

Back

To find the total amount sold after multiple periods of growth, use the formula: Total Sold = Initial Amount * (1 + growth rate)^number of periods.

Front

What is the equivalent expression for 5((1 + 0.02)^12)^3?

Back

The equivalent expression is 5(1.02)^(36). This is derived by multiplying the exponents.

Front

What is the significance of the base in exponential functions?

Back

The base in exponential functions determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.