Unit 5 Review

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What is an exponential decay function?

Back

An exponential decay function is a mathematical function that describes a quantity decreasing at a rate proportional to its current value, often represented as y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you write an equation for a population that decreases by a certain percentage each year?

Back

The equation is written as y = a(1 - r)^t, where 'a' is the initial population, 'r' is the decay 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, 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 population to double?

Back

A population doubles when its size increases by 100%, meaning the new population size is twice the original size.

Front

How do you calculate the future value of an investment?

Back

To calculate the future value of an investment, use the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value (initial investment), r is the annual interest rate (as a decimal), and n is the number of years.

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What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last known term by the common ratio.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

Front

What is the initial value in an exponential function?

Back

The initial value in an exponential function is the value of the function when time (or x) is zero, often represented as 'a' in the equation y = a(b)^x.

Front

How do you express a percentage increase in mathematical terms?

Back

A percentage increase can be expressed as y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the increase rate (as a decimal), and 't' is time.