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if f(x) ia an exponential function where f(-1)=5 and f(7)=32, then find the value of f(4), to the nearest hundredth

Sagot :

sqdancefan

Answer:

  f(4) ≈ 15.95

Step-by-step explanation:

One way to write the function is to start with f(x) = a^x, and do translation and vertical and horizontal scaling on it. The result will be ...

  f(x) = 5(32/5)^((x+1)/8)

  f(4) = 5(32/5)^(5/8) ≈ 15.952637

  f(4) ≈ 15.95

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Additional comment

The template we used for writing an exponential function through two points (x1, y1) and (x2, y2) is ...

  y = y1 · (y2/y1)^((x -x1)/(x2 -x1))

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The attachment shows the result of using a calculator to find an exponential regression curve that matches the given points. Compared to the above, the base of the exponent is (32/5)^(1/8) ≈ 1.26117, and the multiplier is f(0) = 5(32/5)^(1/8) ≈ 6.30583

View image sqdancefan
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