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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.

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Find the equation of the exponential function that passes through the points 1 16 and 1 23 and Use the form y c a x and show how you find the values of and a Sh class=

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mhanifa

Answer:

  • y = 1/3*2^x

Step-by-step explanation:

Given function

  • y = c*a^x

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

Substitute the values of x and y to get the system of equations:

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

Substitute a and solve for c:

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

Find a:

  • a = 6c = 6*1/3 = 2

The equation of the function:

  • y = 1/3*2^x

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