Function f if an exponential function. by what factor does the output value increase as each input value increases by 1? x: -1, 1, 3, 5, 7f(x): 1/4, 6, 64, 1024, 16234

the growth factor is 4

Step-by-step explanation:

We are given f(x) is exponential function

so,

where

a is the initial value

b  is output value increase as each input value increases by 1

so, we have to find 'b'

we can select any two points and then find 'b'

At x=1 , f(x)=4:

we can plug these values

At x=3 , f(x)=64:

we can plug these values

now, we can divide both equations

and we get

we can simplify it

So, the growth factor is 4

sine

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: