1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
valentinak56 [21]
3 years ago
13

Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of

change on the interval (0,3)
Mathematics
1 answer:
victus00 [196]3 years ago
4 0

Answer:

g(x), f(x) and h(x)

Step-by-step explanation:

Given

Interval: (0,3)

See attachment for functions f(x), g(x) and h(x)

Required

Order from fastest to slowest decreasing average rate of change

The average rate of change is calculated as:

Rate = \frac{f(b) - f(a)}{b - a}

In this case:

(a,b) = (0,3)

i.e.

a = 0\\b=3

For f(x)

f(x) = 16(\frac{1}{2})^x

Rate = \frac{f(b) - f(a)}{b - a}

Rate = \frac{f(3) - f(0)}{3 - 0}

Rate = \frac{f(3) - f(0)}{3}

Calculate f(3) and f(0)

f(x) = 16(\frac{1}{2})^x

f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2

f(0) = 16(\frac{1}{2})^0 = 16 * 1 = 16

So:

Rate = \frac{f(3) - f(0)}{3}

Rate = \frac{2 - 16}{3}

Rate = -\frac{14}{3}

For g(x)

Rate = \frac{g(b) - g(a)}{b - a}

Rate = \frac{g(3) - g(0)}{3 - 0}

Rate = \frac{g(3) - g(0)}{3}

From the table of g(x)

g(3) = 1

g(1) = 27

So:

Rate = \frac{1 - 27}{3}

Rate = -\frac{26}{3}

For h(x)

Rate = \frac{h(b) - h(a)}{b - a}

Rate = \frac{h(3) - h(0)}{3 - 0}

Rate = \frac{h(3) - h(0)}{3}

From the graph of h(x)

h(3) = -3

h(0) = 4

So:

Rate = \frac{-3 - 4}{3}

Rate = -\frac{7}{3}

So, the calculated rates of change are:

f(x) = -\frac{14}{3} = -4.67

g(x) = -\frac{26}{3} =-8.67

h(x) = -\frac{7}{3} =-2.33

By comparison:

From the fastest decreasing to slowest, the order is: <em>g(x), f(x) and h(x)</em>

You might be interested in
Megan bought a bicycle that cost $200.50 at a sporting good store. The sales tax
MaRussiya [10]

Answer:

216.9

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What percent of the muffins were carrots
Readme [11.4K]

Answer:

0%

Step-by-step explanation:

Muffins aren't carrots, unless they are carrot muffins.

6 0
3 years ago
Work out the size of angle B
eduard

Answer:

61

Step-by-step explanation:

and let c looks to be a right angle

7 0
3 years ago
Read 2 more answers
For questions 1 - 4, which right triangle congruence theorem can be used to show that the two triangles
SOVA2 [1]

Step-by-step explanation:

1. SAS

2. HL

3. AAS

4 AAS

6 0
3 years ago
In AGHI, the measure of ZI=90°, the measure of ZG=5°, and IG = 57 feet. Find the
xxTIMURxx [149]

Answer:

The answer is 57.2

This is correct

3 0
2 years ago
Other questions:
  • What ahsjsjjkananenhsha
    6·2 answers
  • Stacey filled her 1/2 measuring cup seven times to have enough flour for a cake recipe.How much flour does the cake recipe call
    14·1 answer
  • Which is true about the solution to the system of inequalities shown? y &gt; 3x + 1 y 3x + 1 are solutions. Only values that sat
    12·1 answer
  • Help umm how do i do this im dumb idk how to do it :(
    5·1 answer
  • Which equation has the same solution as x^2 +8x +19=8?
    5·1 answer
  • Can you help me with this thanks
    5·1 answer
  • (order doesn't matter)
    11·1 answer
  • Consider the function.<br> f(x) = 2 x + 12<br> What is the y-intercept of f1(x)?
    14·1 answer
  • You have a part-time job at a deli and work 12 1/2 hours in one week you earn $6.50 per hour how much money do you earn each wee
    14·1 answer
  • Pls help me on this
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!