NoblePenguinidn
Answered

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

Sagot :

Mhanifaidn

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
Supernovaidn

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.

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