Exponents and Exponentials

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is the base in an exponential expression?

Back

The base is the number that is being raised to a power in an exponential expression. For example, in 5^2, 5 is the base.

Front

What is the value of 10^0?

Back

The value of any non-zero number raised to the power of 0 is 1. Therefore, 10^0 = 1.

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, 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 exponential growth mean?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. For example, if a population doubles every year, it is experiencing exponential growth.

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What does exponential decay mean?

Back

Exponential decay refers to the process of reducing an amount by a consistent percentage rate over a period of time. For example, radioactive decay is a common example of exponential decay.

Front

What is a common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to get the next term. For example, in the sequence 2, 6, 18, the common ratio is 3.

Front

How do you calculate the value of an exponential function?

Back

To calculate the value of an exponential function, substitute the value of x into the function and evaluate. For example, for f(x) = 2(4^x), to find f(2), calculate 2(4^2) = 2(16) = 32.

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What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly. For example, y = 2x is linear, while y = 2^x is exponential.

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What is the decay factor in exponential decay?

Back

The decay factor is the amount by which a quantity decreases in each time period. It is always a positive number less than 1. For example, if a quantity decreases by 20% each year, the decay factor is 0.8.