Modeling Functions and Data Patterns

Sally and Sam study turtle populations on three islands in the Florida Keys. They analyze the data using different mathematical functions: linear for Fun Island, exponential for Grape Island, and quadratic for Mystery Island. Each function type is determined by identifying patterns in the data, such as common differences, common ratios, and constant second differences.

What are the names of the three islands being studied for turtle populations?

• Sunny Island, Grape Island, Mystery Island

• Fun Island, Berry Island, Mystery Island

• Fun Island, Grape Island, Mystery Island

• Fun Island, Grape Island, Secret Island

What is the common difference in the turtle population on Fun Island?

• 5 turtles per year

• 2 turtles per year

• 4 turtles per year

• 3 turtles per year

Which type of function is used to model the data from Fun Island?

• Exponential

• Quadratic

• Linear

• Logarithmic

What is the equation for the linear function model of Fun Island?

• y = x + 2

• y = 2x + 3

• y = 2x + 5

• y = 3x + 2

What is the common ratio in the turtle population on Grape Island?

• 4

• 3

• 2

• 1

Which type of function is used to model the data from Grape Island?

• Logarithmic

• Exponential

• Quadratic

• Linear

What is the equation for the exponential function model of Grape Island?

• y = 2^x + 3

• y = 3x^2

• y = 2x + 3

• y = 3 * 2^x

What indicates a quadratic function in the data from Mystery Island?

• A linear pattern

• A common ratio

• A constant second difference

• A constant first difference

Which type of function is used to model the data from Mystery Island?

• Logarithmic

• Linear

• Quadratic

• Exponential

What is the equation for the quadratic function model of Mystery Island?

• y = x^2 + 2x

• y = 2x^2 + x

• y = 3x^2 + 2

• y = 2x + 3