8. the marginal tax rates for a city income tax are as follows: you pay 6% on your earnings up to $100,000…

8. the marginal tax rates for a city income tax are as follows: you pay 6% on your earnings up to $100,000. after that, you pay 2% on earnings greater than $100,000 up to $180,000. for earnings above $180,000, you pay 3.5%. write an equation for the marginal city income tax rate as a function of earnings. fill in the blanks: income = $90,000 → rate = ____ % income = $150,000 → rate = ____ % income = $200,000 → rate = ____ %

8. the marginal tax rates for a city income tax are as follows: you pay 6% on your earnings up to $100,000. after that, you pay 2% on earnings greater than $100,000 up to $180,000. for earnings above $180,000, you pay 3.5%. write an equation for the marginal city income tax rate as a function of earnings. fill in the blanks: income = $90,000 → rate = ____ % income = $150,000 → rate = ____ % income = $200,000 → rate = ____ %

Answer

Explicación:

Paso 1: Analizar los tramos de ingresos

Tenemos tres tramos de ingresos: hasta $100000 se paga un 2%, de $100000 a $180000 se paga un 3.5% y más de $180000 se paga un 6%.

Paso 2: Calcular la tasa para un ingreso de $90000

Como $90000 está en el primer tramo (hasta $100000), la tasa es del 2%.

Paso 3: Calcular la tasa para un ingreso de $150000

El ingreso de $150000 está en el segundo tramo. La tasa es del 3.5%.

Paso 4: Calcular la tasa para un ingreso de $200000

El ingreso de $200000 está en el tercer tramo. La tasa es del 6%.

Paso 5: Escribir la ecuación para la tasa impositiva marginal

Sea $x$ el ingreso. Si $x\leq100000$, $t(x) = 0.02$ Si $100000 < x\leq180000$, $t(x)=0.035$ Si $x > 180000$, $t(x)=0.06$

Respuesta:

Income = $90000 → Rate = 2% Income = $150000 → Rate = 3.5% Income = $200000 → Rate = 6% La ecuación para la tasa impositiva marginal $t(x)$ es: [t(x)=\begin{cases} 0.02, & \text{si } x\leq100000 \ 0.035, & \text{si } 100000 < x\leq180000 \ 0.06, & \text{si } x > 180000 \end{cases}]