NoblePenguin
Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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

Sagot :

mhanifa

Answer:

  • y = 5*2ˣ

Step-by-step explanation:

Exponential function:

  • y = abˣ

Ordered pairs given:

  • (1, 10) and (4, 80)

Substitute x and y values to get below system:

  • 10 = ab
  • 80 = ab⁴

Divide the second equation by the first one and solve for b:

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

Use the first equation and find the value of a:

  • 10 = a*2
  • a = 5

The function is:

  • y = 5*2ˣ
Supernova

Answer:

[tex]y=5 \cdot 2^x[/tex]

Step-by-step explanation:

An exponential function is written in the form:

  • [tex]y=ab^x[/tex]

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 (1, 10) and (4, 80) into the exponential form of a function.

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

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

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

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

  • [tex]10=ab[/tex]
  • [tex]10=a(2)[/tex]
  • [tex]a=5[/tex]

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).

  • [tex]y=5 \cdot 2^x[/tex]

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

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.