Use the table to answer the question.
Time (seconds) 8 9 10 11 12 13 . . .
Height (feet) 14.2 14.55 14.8 14.95 15.0 14.95 . . .
Grace creates a table to track the approximate height reached by her flying disc, in feet, as a function of the time, in seconds, since she released the disc. Determine the type of function that best models the data. What function family does it belong to?
(1 point)
Responses
the linear function family
the linear function family
the cubic function family
the cubic function family
the quadratic function family
the quadratic function family
the square root function family
the square root function family
9 answers
The best type of function that models the data is a quadratic function. It belongs to the quadratic function family.
Given a sequence of data in context where the outputs are constantly increasing but the rate of growth is decreasing, which of the following functions would best model the data? Assume the dataset indicates that there are no relative extrema. (1 point)
Responses
a linear function
a linear function
an absolute value function
an absolute value function
a cubic function
a cubic function
a logarithmic function
Responses
a linear function
a linear function
an absolute value function
an absolute value function
a cubic function
a cubic function
a logarithmic function
A logarithmic function would best model the data in this context where the outputs are constantly increasing but the rate of growth is decreasing.
Juan makes $20 an hour at his job. He creates an equation to predict how much money he will make based on how many hours he works. Determine which function type best models this scenario.(1 point)
Responses
a periodic function
a periodic function
an exponential function
an exponential function
a linear function
a linear function
a quadratic function
a quadratic function
Responses
a periodic function
a periodic function
an exponential function
an exponential function
a linear function
a linear function
a quadratic function
a quadratic function
A linear function would best model this scenario where Juan makes $20 an hour at his job. In a linear function, the output varies directly with the input, so in this case, the amount of money he makes would increase by $20 for each additional hour worked.
Jakeira is a research biologist who is studying a fast-growing bacteria strain of which the population size can double every 8 hours. To predict the colony size over the next week, she creates an equation that relates time in hours to the population size. Which function type best models this scenario?(1 point)
Responses
an exponential function
an exponential function
a periodic function
a periodic function
a linear function
a linear function
a quadratic function
Responses
an exponential function
an exponential function
a periodic function
a periodic function
a linear function
a linear function
a quadratic function
An exponential function would best model this scenario where the population size can double every 8 hours. Exponential growth is characterized by a constant growth rate, in this case, the population doubling every 8 hours.
In Yellowstone National Park, Old Faithful is a geyser that is named because of its consistency. It faithfully erupts on average every 90 minutes. What type of function would best model the water output per minute from Old Faithful?(1 point)
Responses
a linear function
a linear function
a quadratic function
a quadratic function
a periodic function
a periodic function
an exponential function
an exponential function
Responses
a linear function
a linear function
a quadratic function
a quadratic function
a periodic function
a periodic function
an exponential function
an exponential function
A periodic function would best model the water output per minute from Old Faithful, as it erupts on average every 90 minutes in a repeated and consistent pattern. Periodic functions exhibit this repetitive behavior at regular intervals.
1 answer