Question 1151036
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^x = e^(x*(ln(0.9)))}}}
f(x) = {{{x^2 - e^(x*(ln(0.9))) = 0}}}
Differentiate
f'(x) = {{{2x - ln(0.9)*e^(x*(ln(0.9)))}}}
Use Newton-Raphson (or a graphing calculator)
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