Module 1 summative assessment

Which of the contexts below represents exponential decline or decay?

• An elevator descends at a rate of 24 feet per second

• Money invested in a savings account grows at an annual rate of 2.2%

• A car depreciates at a rate of 7.3% per year

• A population of 150 bacteria doubles every minute

Which of the contexts below represents exponential growth?

• Snow was falling at a rate of 1.25 inches per hour

• A car depreciates at a rate of 5.3% per year

• A radioactive compound decays at a rate of 29% per hour

• A certain population of 32 aggressive zombies triples every hour

Which of the contexts below could be modeled by a linear function?

• Money invested in a savings account grows at an annual rate of 2.6%

• A smartphone data plan charges $65/month and $0.46/GB of data used

• A certain population of 24 aggressive zombies quintuples every hour

• A town's population shrinks at a rate of 8.2% every year

The value of a certain investment over time is given in the table below. Determine what kind of function would best fit the data, linear or exponential, and why

• A linear function would best fit the data because as x increases, the y values change additively. The common difference/ slope of this function is approximately 2000.

• A linear function would best fit the data because as x increases, the y values change multiplicatively. The common ratio/ multiplier of this function is approximately 2000.

• An exponential function would best fit the data because as x increases, the y values change additively. The common difference/ slope of the function is approximately 2000

• An exponential function would best fit the data because as x increases, the y values change multiplicatively. The common ratio/ multiplier of the function is approximately 2000

The approximate number of zombies in a certain city over time is given in the table below. Determine if the function would better model the data, linear or exponential, and why

• A linear function would better model the data because as x increases, the y values change additively. Rounded to the nearest .5, the common difference/slope of this function is approximately 109

• A linear function would better model the data because as x increases, the y values change additively. Rounded to the nearest .5, the common ratio/multiplier of this function is approximately 4

• An exponential function would better model the data because as x increases, the y values change multiplicatively. Rounded to the nearest .5, the common ratio/multiplier of this function is approximately 4

• An exponential function would better model the data because as x increases, the y values change additively. Rounded to the nearest .5, the common ratio/multiplier of this function is approximately 109

Determine if the given function on the table is linear or exponential and why.

• An exponential function would better model the data because as x increases, the y values change additively. The common difference/slope of this function is 2

• An exponential function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier of this function is 1/3

• A linear function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier of this function is 1/3

• A linear function would better model the data because as x increases, the y values change additively. the common difference/slope of this function is 2

The estimated population of a certain city over time is given in the table. Determine what kind of function would best fit the data, linear or exponential, and why

• A linear function would better model the data because as x increases, the y values change additively. The common difference/slope of this function is approximately -200

• A linear function would better model the data because as x increases, the y values change additively. The common ratio/multiplier of this function is approximately 0.99

• An exponential function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier of this function is approximately -200

• An exponential function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier of this function is approximately 0.99

The amount of money in a savings account over time is given in the table. Determine what kind of function would better model the data, linear or exponential, and why.

• A linear function would better model the data because as x increases, the y values change additively. The common difference/slope of this function is approximately 160

• A linear function would better model the data because as x increases, the y values change additively. The common ratio/multiplier of this function is approximately 1.59

• An exponential function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier of this function is approximately 1.59

• An exponential function would better model the data because as x increases, the y values change additively. Rounded to the nearest .5, the common ratio/multiplier of this function is approximately 160

Determine what kind of function is depicted in the table below, and why

• This function is exponential because  the ratios of successive y-values are the same.

• This function is  linear because the first differences are constant.

• This function is quadratic because the second differences are constant.

• This function is neither linear, quadratic, or exponential because  there is no pattern.

Determine what kind of function is depicted in the table below, and why

• This function is exponential because  the ratios of successive y-values are the same.

• This function is  linear because the first differences are constant.

  
  

• This function is quadratic because the second differences are constant.

• This function is neither linear, quadratic, nor exponential because  there is no pattern.