exponential and logarithmic functions pre-test

Front

What is the domain of the function f(x) = log₂(x)?

Back

Domain: x > 0

Front

What is the range of the function f(x) = log₂(x)?

Back

Range: all real numbers

Front

What is the value of log₅(25)?

Back

2

Front

If a town doubles its size every 33 years, what will be the population in 66 years if it starts at 6,000?

Back

24,000

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.

Front

If $5000 is deposited at an interest rate of 4.75% compounded monthly, what will the balance be after 35 years?

Back

$26,276

Front

What is the inverse of the logarithmic function f(x) = logₐ(x)?

Back

The inverse is f⁻¹(x) = a^x.

Front

What does the term '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.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number.

Front

How do you convert a logarithmic equation to an exponential equation?

Back

If logₐ(b) = c, then it can be rewritten as a^c = b.