F. of Math 3 Mid Unit 2 Review for Test

Front

What is the formula for compound interest?

Back

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

How do you calculate the population after a percentage decrease?

Back

Use the formula: P = P0(1 - r)^t, where P0 is the initial population, r is the rate of decrease (as a decimal), and t is the time in years.

Front

What is the relationship between exponents in the equation 3^(2x) = 27^(x - 4)?

Back

Since 27 can be expressed as 3^3, the equation can be rewritten as 3^(2x) = 3^(3(x - 4)). This allows us to set the exponents equal to each other: 2x = 3(x - 4).

Front

What does it mean to solve an equation for x?

Back

To solve an equation for x means to find the value of x that makes the equation true.

Front

What is the formula for exponential growth?

Back

The formula is y = a(1 + r)^t, where y is the final amount, a is the initial amount, r is the growth rate (as a decimal), and t is the time.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 35% becomes 0.35.

Front

What is the initial amount in the function y = 15(1.35)^x?

Back

The initial amount is 15, which represents the starting value before any growth occurs.

Front

How do you find the value of x in a logarithmic equation?

Back

To find x in a logarithmic equation, you can rewrite the equation in exponential form or use logarithmic properties to isolate x.

Front

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

Back

The future value (FV) can be calculated using FV = PV(1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.

Front

What does a 6% annual decrease mean in terms of population?

Back

A 6% annual decrease means that each year, the population will be 94% of the previous year's population.