Exponential and Logarithmic Functions Practice Test

What is the decay factor for a substance that halves every four years?

• 0.5

• 2

• 0.25

• 1.5

If a population increases by 20% annually, what would be the growth factor used in the formula?

• 1.2

• 0.8

• 1.0

• 1.5

How do you calculate the amount of a radioactive substance left after a certain number of years given its half-life?

• Initial amount * (1/2)^(years/half-life)

• Initial amount / (2)^(years/half-life)

• Initial amount * (2)^(years/half-life)

• Initial amount / (1/2)^(years/half-life)

What is the inverse function of y = 5^x?

• y = log base 5 of x

• y = 5 * log of x

• y = x^5

• y = 5/x

For an investment that doubles every 7 years, what is the formula to calculate its future value?

• Initial amount / (2)^(years/7)

• Initial amount / (2)^(7/years)

• Initial amount * (2)^(7/years)

• Initial amount * (2)^(years/7)

What is the result of solving the equation 2x + 3 = 7?

• x = 5

• x = 4

• x = 3

• x = 2

Which function type is typically used to model growth that halves over regular intervals?

• Exponential growth

• Exponential decay

• Linear function

• Quadratic function

If the base of a logarithm is increased, what happens to the value of the logarithm for the same input?

• It remains the same

• It decreases

• It becomes zero

• It increases

What is the primary reason for using logarithms in calculating the magnitude of earthquakes?

• To simplify multiplication

• To convert multiplicative relationships into additive ones

• To increase calculation speed

• To decrease the value of outputs

In a geometric sequence, if the common ratio is 1/2, what is the fourth term given the first term is 16?

• 16

• 8

• 4

• 2