Week 06 - Bell Ringer 2

Aliyah is using a calculator app on her smartphone that has a 'reverse' button. What is the function of this 'reverse' button?

• A function that has no output

• A function that performs the same action as another function

• A function that undoes the action of another function

• A function that only works for certain inputs

Answer explanation

An inverse function is a function that undoes the action of another function.

Emmanuel is working on a research project about the growth of yeast cells in a lab culture. He observes that the yeast population decreases at certain times due to environmental factors. To calculate the time it takes for the yeast population to decrease to half its size, which mathematical operation should he use?

• Divide the time by the decay rate

• Calculate the logarithm of the population using the decay rate as the base

• Multiply the initial population by the decay rate

• Raise the decay rate to the power of time

Answer explanation

The inverse of an exponential expression is obtained by switching the base and the exponent. This allows us to find the original value from the result of the exponential expression.

Beatriz is working on a science experiment where she needs to convert the logarithmic expression log₃(81) to its equivalent exponential form to understand the growth of bacteria. What is this process called?

• exponentiation

• logarithmization

• logarithmic conversion

• logarithmic transformation

Answer explanation

The process of converting logarithmic expressions to exponential form is called exponentiation. It involves raising the base to the power of the logarithm.

Jacob is helping Noe with a math assignment where they need to convert the logarithmic expression log₃(81) to its equivalent exponential form. Which of the following is the correct conversion?

• 3^x = 81

  where x = 4

• x^3 = 81

  where x = 4

• 81^3 = x

  where x = 4

• 3^81 = x

  where x = 4

Answer explanation

The process of converting logarithmic expressions to exponential form is called exponentiation. It involves raising the base to the power of the logarithm.

Jazlyn, Santiago, and Bryan are working on a video project. Jazlyn records the footage, Santiago edits the video, and Bryan adds special effects to the edited video. What does this scenario represent in terms of function composition?

• Jazlyn applying her recording function to her own output

• Jazlyn and Santiago applying their functions to the same footage

• Santiago applying his editing function to the result of Jazlyn's recording function, and Bryan applying his special effects function to the result of Santiago's editing function

• Bryan applying his special effects function to a random video

Answer explanation

The composition of functions is applying one function to the result of another function. This choice correctly describes the concept.

Joselyn, Jada, and Zaid are working on a science project about the universe. Joselyn asks, 'If we were to model the expansion of the universe over time, what would be the inverse of a logarithmic expression that we could use to estimate the size of the universe at a given time in the past?'

• An exponential expression

• A trigonometric expression

• A linear expression

• A quadratic expression

Answer explanation

The inverse of a logarithmic expression is an exponential expression.

Nancy is monitoring the population growth of a yeast colony in her biology project. She has the exponential growth equation and is interested in calculating the growth rate. What is the name of the process for transforming the exponential growth equation into logarithmic form to determine this rate?

• Taking the logarithm

• Simplifying

• Expanding

• Factoring

Answer explanation

The process of converting exponential expressions to logarithmic form is called taking the logarithm. It involves finding the exponent when a given base is raised to a certain power.

Marilyn and Bryan are studying functions in their math class. Marilyn comes across a function f(x) and Bryan finds its inverse g(x). If Bryan applies g(x) to a certain expression, what result should he expect?

• 2

• 3

• 24

• None

If g(x) is an inverse of below f(x) then Select the right choice for g(x)

• 
• 
• 
• 

Beatriz, Jazlyn, and Marco are trying to solve for x in the real-world function f(x) that represents the cost of items in dollars. They need to select all the right choices of x where the function f(x) equals 3 dollars.

• 1

• 2

• -3.5

• 3

• 10