Question

Which situation is best modeled by a nonlinear function with time as the independent variable? A. an investment that increases by a constant factor of 1.05, or by 5%, every year B. an investment that increases by $25 every year C. an investment that takes 2 years to increase in value by $40 and 5 years to increase in value by $100 D. an investment that increases by $1 every 5 weeks

Answer 1

The situation that is best modeled by a nonlinear function with time as the independent variable is option C: an investment that takes 2 years to increase in value by $40 and 5 years to increase in value by $100.

A nonlinear function is a function that does not have a constant rate of change, which means that its graph is not a straight line. In option C, the investment increases in value at a different rate over different time periods, which makes it a nonlinear function.

Option A represents an investment that increases by a constant factor of 1.05, or by 5%, every year, which can be modeled by an exponential function. Option B represents an investment that increases by a constant amount every year, which can be modeled by a linear function. Option D represents an investment that increases by a constant amount every 5 weeks, which can also be modeled by a linear function.

Therefore, option C is the best situation to be modeled by a nonlinear function with time as the independent variable.