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
Simply using exponents .Then find the products .
aksik [14]

Answer:

\sqrt[7]{b^{15}}

Step-by-step explanation:

=> b^2*\sqrt[7]{b}

=> b^2*b^{1/7}

Where bases are same, powers are to be added.

=> b^{2+(1/7)}

=> b^ {14+1/7}

=> b^{15/7}

=> \sqrt[7]{b^{15}}

6 0
3 years ago
Pom
777dan777 [17]
Am not sure but Y=-x+2
4 0
3 years ago
Draw an angle of 40 degree. copy it's supplementary angle
Mila [183]
This is the correct form of a supplementary angle. 

3 0
3 years ago
A student.masteryconnect.com
Crazy boy [7]
We can’t click on the link maybe take a pic
4 0
2 years ago
The Smith family is shopping for a new car and they are basing their decision on color and style. Explain how many color choices
Yanka [14]
Sample response: The Smith family has 2 choices to make, color and style. By the fundamental counting principle, the product of the number of choices of color and style must equal 8. So, there could be 1 color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles, or 8 colors and 1 style.
3 0
3 years ago
Read 2 more answers
Other questions:
  • HELP PLEASE! Can you please explain so I can understand how it was completed?
    7·1 answer
  • Two hundred thirty million, three hundred forty-four thousand, nine hundred ninety-six
    5·1 answer
  • Find the set of outcomes that occur when we flip 3 coins and obtain more heads than tails<br> .
    9·1 answer
  • Help me please in inequalities
    5·1 answer
  • How many solutions does the equation have?
    5·1 answer
  • Convert the improper fraction to a mixed number.
    10·1 answer
  • Over the course of a year, a company goes from 115 employees to 124 employees. Use the drop-down menus to build an equation that
    5·1 answer
  • In 2001, one county reported that, among 3132 white women who had babies, 94 were multiple births. There were also 20 multiple b
    6·1 answer
  • The intersection of roads M and N creates a 41.4 degree angle. What are the complimentary and supplementary angles of this inter
    10·1 answer
  • Gabriel tossed a paper cup 40 times and recorded how the cup landed each time. He organized the results in the table shown. Find
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!