SOLUTION: Find the intersections of y=x^2 and y=0.9^x

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Question 1151036: Find the intersections of y=x^2 and y=0.9^x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the intersections of y=x^2 and y=0.9^x
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x^2 = 0.9^x
x^2 - 0.9^x = 0
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There is no algebraic solution since x is in a term and in an exponent.
Use graphical or iterative methods.
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0.9%5Ex+=+e%5E%28x%2A%28ln%280.9%29%29%29
f(x) = x%5E2+-+e%5E%28x%2A%28ln%280.9%29%29%29+=+0
Differentiate
f'(x) = 2x+-+ln%280.9%29%2Ae%5E%28x%2A%28ln%280.9%29%29%29
Use Newton-Raphson (or a graphing calculator)
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