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Find the inverse of your exponential function y= 6995(.85)^x

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[tex]y= \frac{\ln(\frac{x}{6995}) }{\ln (.85)}[/tex]

Taking the original function, swap the x and y.

y = 6995(.85)^x  ----> x = 6995(.85)^y

Solve for y.

Divide both sides by 6995.

x/6995 = (.85)^y

Take the natural log of both sides.

ln (x/6995) = ln (.85)^y

Apply the property of logarithms where log a^b = b log a.

ln (x/6995) = y ln (.85)

Divide both sides by ln (.85) to get y.

y = ( ln ( x / 6995)) / ln (.85)

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