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受欢迎的代数 >

A(x)=500(1.03)^x

解答

A (x) = 500 (1.03)^{x}

解答

x = - \frac{W ( - \frac{500 l n ( 1.03 )}{A} )}{ln ( 1.03 )}

求解步骤

A (x) = 500 (1.03)^{x}

将

A (x) = 500 (1.03)^{x}

调整为朗伯形式:

A x e^{- l n (1.03) x} = 500

用

- x ln (1.03) = u

和

x = - \frac{u}{ln ( 1.03 )}

改写方程式

A (- \frac{u}{ln ( 1.03 )}) e^{u} = 500

改写

A (- \frac{u}{ln ( 1.03 )}) e^{u} = 500

为朗伯形式:

e^{u} u = - \frac{500 ln ( 1.03 )}{A}

解

e^{u} u = - \frac{500 ln ( 1.03 )}{A} : u = W (- \frac{500 ln ( 1.03 )}{A})

u = W (- \frac{500 ln ( 1.03 )}{A})

代回

u = - x ln (1.03)

，求解

x

解

- x ln (1.03) = W (- \frac{500 ln ( 1.03 )}{A}) : x = - \frac{W ( - \frac{500 l n ( 1.03 )}{A} )}{ln ( 1.03 )}

x = - \frac{W ( - \frac{500 l n ( 1.03 )}{A} )}{ln ( 1.03 )}

作图

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