Question

need help quickly !! which of the given functions have an average rate of change of -12 on the interval [0,2]?

Answer 1

Option 1 and Option 3 are correct.

Step-by-step explanation:

We need to find the functions that have rate of change of -12 on the interval [0,2]

The formula used to find rate of change is:

$Rate\,\,of\,\,Change=\frac{f(b)-f(a)}{b-a}$

where a =0 and b=2

Checking all options and finding which options have Rate of change =-12 over interval [0,2]

Option 1:

$f(x)=-3(3^x)$

f(a)=f(0)=-3(3^0)=-3(1)=-3

f(b)=f(2)=-3(3^2)=-3(9)=-27

Finding rate of change:

$Rate\,\,of\,\,Change=\frac{-27-(-3)}{2-0}\\Rate\,\,of\,\,Change=\frac{-27+3}{2}\\Rate\,\,of\,\,Change=\frac{-24}{2}\\Rate\,\,of\,\,Change=-12$

Rate of change = -12

Option 1 is correct.

Option 2:

$f(x)=12x-\frac{2}{3}$

f(a)=f(0)=12(0)-2/3=0-2/3=-2/3=-0.6

f(b)=f(2)=-12(2)-2/3=-24-2/3=-24*3-2/3=-72-2/3=-74/3=-24.6

Finding rate of change:

$Rate\,\,of\,\,Change=\frac{-24.6-(-0.6)}{2-0}\\Rate\,\,of\,\,Change=\frac{-27+0.6}{2}\\Rate\,\,of\,\,Change=\frac{-26.4}{2}\\Rate\,\,of\,\,Change=-13.2$

Rate of change = -13.2

Option 2 is incorrect.

Option 3:

$f(x)=-5^x$

f(a)=f(0)=-5^0= -1

f(b)=f(2)=-5^2= -25

Finding rate of change:

$Rate\,\,of\,\,Change=\frac{-25-(-1)}{2-0}\\Rate\,\,of\,\,Change=\frac{-25+1}{2}\\Rate\,\,of\,\,Change=\frac{-24}{2}\\Rate\,\,of\,\,Change=-12$

Rate of change = -12

Option 3 is correct.

Option 4:

$f(x)=-12^x$

f(a)=f(0)=-12^0=-1

f(b)=f(2)=-12^2=-144

Finding rate of change:

$Rate\,\,of\,\,Change=\frac{-144-(-1)}{2-0}\\Rate\,\,of\,\,Change=\frac{-144+1}{2}\\Rate\,\,of\,\,Change=\frac{-143}{2}\\Rate\,\,of\,\,Change=-71.5$

Rate of change = -71.5

Option 4 is incorrect.

Option 5:

$f(x)=\frac{-1}{12}x+9$

f(a)=f(0)=-1/12(0)+9=0+9=9

f(b)=f(2)=-1/12(2)+9=-1/6+9=-1+9*6/6=-1+54/6=53/6=8.83

Finding rate of change:

$Rate\,\,of\,\,Change=\frac{8.33-(9)}{2-0}\\Rate\,\,of\,\,Change=\frac{8.33-9}{2}\\Rate\,\,of\,\,Change=\frac{-0.67}{2}\\Rate\,\,of\,\,Change=-0.335$

Rate of change = -0.335

Option 5 is incorrect.

Option 6:

$f(x)=7-12x$

f(a)=f(0)=7-12(0)=7-0=7

f(b)=f(2)=7-12(2)=7-24=-17

Finding rate of change:

$Rate\,\,of\,\,Change=\frac{-17-(-7)}{2-0}\\Rate\,\,of\,\,Change=\frac{-17+7}{2}\\Rate\,\,of\,\,Change=\frac{-10}{2}\\Rate\,\,of\,\,Change=-5$

Rate of change = -5

Option 6 is incorrect.

So, Option 1 and Option 3 are correct.

Keywords: Rate of change

Learn more about Rate of change at:

• brainly.com/question/5922969
• brainly.com/question/10699220
• brainly.com/question/3071107

#learnwithBrainly