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shtirl [24]
3 years ago
6

Find the equation of the exponential function that passes through the points (- 1, 1/6) and (1, 2/3) and Use the form y = c * a

^ x and show how you find the values of and a. Show all work , not just the final equation.
Will give Brainliest to the right answer with steps

Mathematics
1 answer:
icang [17]3 years ago
8 0

Answer:

  • y = 1/3*2^x

Step-by-step explanation:

<u>Given function</u>

  • y = c*a^x

The points (-1, 1/6) and (1, 2/3) lie on the graph

<u>Substitute the values of x and y to get the system of equations:</u>

  • 1/6 = c*a^(-1) ⇒ 1/6 = c/a ⇒ a = 6c
  • 2/3 = c*a^1 ⇒ 2/3 = ac

<u>Substitute a and solve for c:</u>

  • 2/3 = 6c*c
  • 1/9 = c²
  • c = √1/9
  • c = 1/3

<u>Find a:</u>

  • a = 6c = 6*1/3 = 2

<u>The equation of the function:</u>

  • y = 1/3*2^x

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