Exponential and Logarithmic Regression Models

A single person sent a text to 3 friends. Each person in this group of 3 people then sent the same text to several people. In each subsequent stage, each person who received a text sent the text to several new people. The table shows the number of texts sent at each stage.

Using regression methods, write the function that BEST represents this data?

• f(x) = .9(4)^x

• f(x) = 1.3(3)^x

• f(x) = 152x - 176

• f(x) = 73x² - 213x + 68

What type of function BEST models this data, and why?

• Linear, because it should change at a constant rate.

• Quadratic, because it will be curved and should change direction.

• Exponential, because it should curve, but always moving in the same direction.

• Logarithmic, because this wasn't discussed and I like to guess.

Using regression methods, write the function that BEST represents this data?

• V = -1053y + 14,413

• V = 60y² - 1,500y + 15,000

• V = 15,000(0.9)^y

• V = 100y² - 1,200y + 15,000

Jackson, Aria, and Harper are studying the population growth of a certain species of bacteria. They notice that the population growth does not seem to be linear, but rather, it seems to be growing at an increasing rate. Which concept could they use to model this type of growth?

• They could use exponential regression, which models the relationship between equal-length input intervals and proportional output intervals.

• They could use exponential regression, but it is only applicable to discrete data.

• They could use exponential regression, which models the relationship between equal-length input intervals and linear differences in outputs.

• They could use exponential regression, which is used to model linear relationships between variables.

Is the table linear, exponential, or quadratic?

• Linear

• Exponential

• Quadratic

• none of these

Given the table, determine the equation of the function. 

• y = 4(4)^x

• y = 4(¼)^x

• y = 4(x-0)² + 4

• y = 2(x-1)² + 16

What function model best represents the data in the table?

• linear

• exponential

• quadratic

A chemist has a 100-gram sample of a radioactive material.  He records the amount of radioactive material every week for 6 weeks and obtains the following data: Find the exponential model of the function.

• y = 100(8.7)^x

• y = 100(1.87)^x

• y = 100(.87)^x

• y = 100(.13)^x

Which statements describe the value of the car as a function of x, its age in years? Check all that apply.

• The relationship is quadratic.

• The relationship is exponential.

• The domain is {x| x < 0}.

• The range is {V | 0 < V < 20,000}.

• The value, V, is represented by the equation V = 20,000(0.9)^x.

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions