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
SIZIF [17.4K]
2 years ago
5

The graph of an exponential function passes through (1, 10) and (4, 80). Find the function that describes the graph.

Mathematics
2 answers:
Otrada [13]2 years ago
7 0

Answer:

y=5 \cdot 2^x

Step-by-step explanation:

An exponential function is written in the form:

  • y=ab^x

We can use the given points that the exponential function passes through to solve for a and b.

Create a system of equations by substituting <u>(1, 10)</u> and <u>(4, 80)</u> into the exponential form of a function.

  • \text{I}:\ 10=ab^1
  • \text{II}: \ 8 0=ab^4

Divide Equation I by Equation II in order to cancel out variable a.

  • \displaystyle \frac{80=ab^4}{10=ab}
  • 8=b^3
  • b=2

Now we can solve for a by substituting b back into either equation from the system of equations.

  • 10=ab
  • 10=a(2)
  • a=5

Substitute 5 for a and 2 for b into the form of an exponential function to find the exponential function that passes through (1, 10) and (4, 80).

  • y=5 \cdot 2^x

y = 5 · 2ˣ is the exponential function that describes the graph.

svetlana [45]2 years ago
4 0

Answer:

  • y = 5*2ˣ

Step-by-step explanation:

<u>Exponential function:</u>

  • y = abˣ

<u>Ordered pairs given:</u>

  • (1, 10) and (4, 80)

<u>Substitute x and y values to get below system:</u>

  • 10 = ab
  • 80 = ab⁴

<u>Divide the second equation by the first one and solve for b:</u>

  • 80/10 = b³
  • b³ = 8
  • b = ∛8
  • b = 2

<u>Use the first equation and find the value of a:</u>

  • 10 = a*2
  • a = 5

<u>The function is:</u>

  • y = 5*2ˣ
You might be interested in
Can someone help me with this math problem ​
Arte-miy333 [17]

Answer:

5370

Step-by-step explanation:

8 0
3 years ago
7b minus 3 how do you say that question
Mumz [18]
Uhhhh... I think you just said it, elsewhere, 7 * b - 3
7 0
3 years ago
Read 2 more answers
What is 5 multiplied by 3 1/4 as a mixed number or a mixed number
Travka [436]

Answer:

65/4

Step-by-step explanation:


3 0
3 years ago
Read 2 more answers
Solve the literal equation for c 4p+9c=p
zimovet [89]

4p+9c=p

move 4p to the other side

sign changes from +4p to -4p

4p-4p+9c=p-4p

9c= p-4p

9c= -3p

divide both sides by 9 to get c by itself

9c/9= -3p/9

c= -3p/9

reduce by dividing by 3

-3p/3= -p

9/3= 3

Answer:

c= -p/3

5 0
3 years ago
Read 2 more answers
Solve for W <br> Simplify as much as possible <br><br> 5(w+3)=50<br><br> :’) help meh plz
Nata [24]

5(w + 3) = 50 \\  \\ 5w + 15 = 50 \\  \\ 5w = 50 - 15 \\  \\ 5w = 35 \\  \\ w =  \frac{35}{5}  \\  \\ w = 7

# be care#

7 0
2 years ago
Read 2 more answers
Other questions:
  • What is 15/50 in simplest form
    13·1 answer
  • Please solve this problem and show your work !! Please answer this !!
    15·1 answer
  • <img src="https://tex.z-dn.net/?f=54x2y%20-%2012x2y2" id="TexFormula1" title="54x2y - 12x2y2" alt="54x2y - 12x2y2" align="absmid
    9·2 answers
  • ETF is an example of
    7·1 answer
  • A rectangular field has an area of 162 m2.
    11·2 answers
  • Multiply. Do not round your answer.<br><br> 6.9 × 1.221 = <br><br><br> Thanks :D
    6·1 answer
  • Solve for theta to the nearest degree​
    5·1 answer
  • 3/4 of the class are girls. 1/6 of the girls have long hair. What fraction of the class with long hair? Place your answer in sim
    14·1 answer
  • What is the answer to this?
    14·1 answer
  • PLEASE HELP ASAP
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!