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Find the equation of the exponential function, in y=a(b)^x form that passes through the points (-2,3) and (6,35). Round both a and b to the nearest hundredth. Must be an algebraic method.

Respuesta :

xEngineerOrg
I supose your function is: [tex]y(x)=a \cdot b^x[/tex]

Step 1. Replace the coordinates of the first point in your equation:
x=-2, y=3

[tex]3=a \cdot b^{-2}[/tex]

Solve the equation for "a":
[tex]a=3 \cdot b^2[/tex]

Step 2. Replace the coordinates of the second point in your equation:
x=6, y=35

[tex]35 = a \cdot b^6[/tex]

Replace the value of "a" from Step 1.
[tex]35 = 3 \cdot b^2 \cdot b^6[/tex]
Calculate "b":
[tex]b= \sqrt[8]{\frac{35}{3}} = 1.359466[/tex]

Step 3. Replace "b" in first equation and calculate "a":
[tex]a=3 \cdot b^2=5.5444434[/tex]

The equation is:
[tex]y(x)=5.54 \cdot 1.36^x[/tex]

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