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
charle [14.2K]
3 years ago
5

Between x=2 and x=3, which function has a greater average rate of change than f(x)=2^x has?

Mathematics
1 answer:
maxonik [38]3 years ago
4 0

Answer: f(3)

Step-by-step explanation:

First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

y=2^x\\\ln(y)=x \ln(2)

Implicitly differentiate the left side and take the derivative of the right side

\frac{y'}{y} =\ln(2)

Multiply both sides by 'y' which was defined as 2^x

y'=\ln(2)*2^x

Plug in x = 2 and x = 3 to see which slope is larger

y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)

You might be interested in
Kelly blends coffee. She mixes brand A costing $6 per kilogram with brand B costing $8 per kilogram. How many kilograms of each
sukhopar [10]

Step-by-step explanation:

Let

x

be the kg of coffee of brand A in the mix and

y

be the kg of coffee of brand B in the mix.

The total kg must be

50

.

x

+

y

=

50

The cost per kg of the mix must br

$

7.20

. For this, the total cost of the mix will be

6

x

+

8

y

, so the total cost per kg of the mix will be

6

x

+

8

y

50

.

6

x

+

8

y

50

=

7.20

Now that we have our two equations, we can solve.

6

x

+

8

y

=

7.20

⋅

50

6

x

+

8

y

=

360

From the first equation, we can multiply both sides by

6

to get:

6

x

+

6

y

=

300

Subtracting, we get:

2

y

=

60

y

=

30

Thus, we need

30

kg of brand B in our mix. This means that

50

−

30

=

20

kg will be of brand A.

6 0
2 years ago
The table and graph both represent
valina [46]

I'm not sure what your table and graph look like but they might both represent the relationship between numbers, like the common difference (+5 ect) They could also both represent  positive growth or negative growth depending on how the graph and table look.

Hope this helps!

8 0
2 years ago
Why do you add a zero when multiplying two digits by two digits
malfutka [58]
When you add a zero to the problem, it shows you are now multiplying in the double-digits. Let's say you are multiplying 12x12. First you cover up the one then multiply them. Then cover up the two and you have 10. When you multiply them, it ends in a zero. Don't think of it as adding a zero but adding to products.
6 0
3 years ago
Francis earns $3.50 an hour mowing lawns. He also gets a $10.00 a week allowance. Bella earns $5.25 an hour babysitting and spen
Alika [10]
3.5h+10=5.25h-11
21=1.75h
12=h

3.5(12)+10=5.25(12)-11
52=52
8 0
3 years ago
Simplify 4+(-3)-2 times (-6)
zloy xaker [14]
<span><span>4−3</span>−<span><span>(2)</span><span>(<span>−6</span>)</span></span></span><span>=<span>1−<span><span>(2)</span><span>(<span>−6</span>)</span></span></span></span><span>=<span>1−<span>(<span>−12</span>)</span></span></span><span>=<span>13</span></span>
6 0
3 years ago
Read 2 more answers
Other questions:
  • The order of magnitude for the population of the United States is 8.
    14·2 answers
  • How do you do this 9x-3=5x-15?
    14·1 answer
  • Graph f(x)=12x+2.i need help
    14·1 answer
  • What are they?<br> Equal Lines?<br> Parallel Lines?<br> perpendicular Lines?<br> None of the above?
    11·1 answer
  • Please help I’ll give 50 points
    12·2 answers
  • (x + 3)^2 - 4x^2<br><br> Factorise using the difference of two squares
    13·1 answer
  • In the diagram, line r is parallel to BC.
    15·2 answers
  • What is this??? 28÷7×4=?
    7·1 answer
  • Please help! 30 points!
    14·2 answers
  • Help???? I can’t figure this out
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!