Question

Compare and contrast exponential and linear functions using both graphs and tables. How would you determine if a function is linear or exponential by looking only at a table?

Answer 1

Exponential: the input and output values do not create equivalent ratios when compared, the out gains faster over time.

Linear: the input and output gain at the same rate, and create equivalent ratios when compared.

You can tell if a function in a table is linear by seeing if the output gains the same number each time.

Explanation:

Answer 2

The main difference between the linear and exponential function is the following: the linear function f(x)=ax+b is changing at a constant rate as x changes and the exponential function f(x)=ab^x is changing at a rate that's always proportional to the value of the function. Using both graphs and tables can be notices that exponential growth is far more significant than linear growth. By looking only at a table we can determine if a function is linear of exponential by determining which growth is more significant (the exponential function has far more significant growth than the linear function).