Question

Which rule can be used to describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3?

Answer 1

The rule "multiply by 12" describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3.

Explanation:

The given function is

`y=12^x`

The initial value is 1 and the growth factor is 12.

It is an exponential function.

At x=-1

`y=12^(-1)=(1)/(12)`

At x=0

`y=12^(0)=12^(-1)* 12=1`

At x=1

`y=12^(1)=1 * 12=12`

At x=2

`y=12^(2)=12 * 12=144`

At x=3

`y=12^(3)=144 * 12=1728`

Therefore the rule "multiply by 12" describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3.

Answer 2

"Which rule ..." suggests you have some rules to choose from to describe the growth. Since you refer to "each interval from x=-1 to x=3", we assume your rule is concerned with more than one interval. With no further clues as to what you may be looking for, we can compute the factor by which the function grows from x=-1 to x=3.

The growth factor over that interval is the ratio of final value to initial value:

.. (12^3)/(12^-1) = 12^(3 -(-1)) = 12^4 = 20,736