Exponential and Logarithmic Functions Test Review

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What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to a rapid increase. Example: Population growth can be modeled by the function y = a(1 + r)^t, where r is the growth rate.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. Example: Radioactive decay can be modeled by the function y = a(1 - r)^t, where r is the decay rate.

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, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does the variable 'a' represent in the logarithmic function y = a*log_b(x-h)+k?

Back

In the logarithmic function, 'a' represents the vertical stretch or compression and reflection of the graph. If 'a' is greater than 1, the graph is stretched; if '0 < a < 1', it is compressed; if 'a' is negative, the graph is reflected.

Front

What is the horizontal asymptote of the function y = a*b^x?

Back

The horizontal asymptote of the function y = a*b^x is y = 0, as x approaches negative infinity for exponential growth (b > 1) or y = a if b < 1 (exponential decay).

Front

How do you identify exponential growth from a function?

Back

Exponential growth can be identified if the base of the exponent is greater than 1 in the function y = a*b^x, where b > 1.

Front

How do you identify exponential decay from a function?

Back

Exponential decay can be identified if the base of the exponent is between 0 and 1 in the function y = a*b^x, where 0 < b < 1.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, denoted as ln(x). It is used in various applications, including growth and decay problems.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

Front

What is the value of log_b(b)?

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The value of log_b(b) is 1, because b raised to the power of 1 equals b.