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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
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