Question

Graph these two functions on the graphing calculator: y = 3x2 and y = 3x Based on the graphs on your calculator, which function appears to grow faster?

Answer 1

The exponential function.

Explanation:

The exponential function increases faster because any number that has an exponent will be larger than a linear or quadratic equation. For example, lets use y = 3x^2 and y = 3^x. Lets input the value of x as 7. Now lets plug it in.

Quadratic equation: y = 3(7)^2 = 21^2 = 441.

Exponential equation: y = 3^7 = 2187

You can see that the exponential value is much larger than the quadratic.

Therefore, exponential always increases at a faster rate.

Answer 2

Well if you meant write y =3x^2 then it is an exponential function. exponential functions will always decrease or decrease faster than a linear function. If you meant to write y = 3x+2 then they would increase at the same rate since the slope of the two linear equations are the same