NoblePenguin
Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.