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
Aleonysh [2.5K]
2 years ago
15

Two functions are shown below.

Mathematics
2 answers:
vodka [1.7K]2 years ago
6 0

Answer:

  x = 6

Step-by-step explanation:

We assume your functions are ...

  • f(x) = (1/2)(2^x)
  • g(x) = 5x+2

In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.

__

Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.

<em>Check</em>: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2

__

<em>Additional comment</em>

We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...

  f(x) -g(x) = 0

Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.

For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.

The lower value of x where the graphs cross is an irrational number near −0.319886722135.

ELEN [110]2 years ago
5 0

Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

You might be interested in
Given that 5x:9=7:3 calculate the value of x. give your answer in its simplest form.
Hitman42 [59]

\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}

<h3>x = 21/5</h3>

Step-by-step explanation:

<h3>___________________________</h3>

<h3>Given →</h3>

5x:9 = 7:3

<h3>So,</h3>

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

<h3>___________________________</h3>

<h3>Hope it helps you!!</h3>
8 0
1 year ago
2x+5=15<br><br> Solve for x<br> a.5<br> b.2<br> c.7<br> d.10
Black_prince [1.1K]

Answer:

A.5

Step-by-step explanation:

3 0
2 years ago
PLZ HELP NOW PLZ PLZ
anyanavicka [17]

Answer:

16ft i think

Step-by-step explanation:

7 0
2 years ago
Whats the equation help pls.
garik1379 [7]

Answer:

One bottle cost 0.41 cents

Step-by-step explanation:

5.89 - 3.43 = 2.46

2.46 divided by 6 = 0.41

I did not add tax.

6 0
3 years ago
What is the height of the tree?
Nataly [62]

Answer:

The tree is 16 ft tall

3 0
3 years ago
Other questions:
  • Greta made the following scores on her first semester history tests: 60, 84, 88, 94, 94, 96. Which measure would she use in summ
    15·2 answers
  • Which equation is related to 58 = x + 25?
    9·2 answers
  • Hey can someone answer this ASAP
    9·1 answer
  • The angle of the roof is 56 she built the doll house with a scale of 1:4 what is it measured
    5·1 answer
  • James thinks the perimeter of this figure is 6x + 10. Ana thinks it is 6x + 6. Who is
    12·1 answer
  • You are graphing Rectangle ABCD in the coordinate plane. The following are three of the vertices of the rectangle: A (2,1), B (5
    11·1 answer
  • Using this graph as a reference, what is the solution for this system of equations?
    12·1 answer
  • Help!! Willmark brainliest!Can you guys please answer these 2 questions???
    5·1 answer
  • Use long to divide 34298 by 26 then select the true statement the quotient has a remainder of 4 the quotient has a remainder of
    5·1 answer
  • Three (3) is a common factor of 21 and 22.<br> O A. True<br> B. False<br> SUBMIT
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!