the laffer curve was originated by the economist arthur laffer to describe revenue from taxes in terms of…

the laffer curve was originated by the economist arthur laffer to describe revenue from taxes in terms of the tax rate. a function that might describe the entire laffer curve is given by y = x(100 - x)(x² + 400), where y is government revenue in hundreds of thousands of dollars from a tax rate of x percent, with the function valid for 0 ≤ x ≤ 100. find the revenue from the following tax rates. (a) 10% (b) 30% (c) 50% (d) 80% (e) graph the function. (a) the revenue from a tax rate of 10% is billion dollars. (simplify your answer.)

the laffer curve was originated by the economist arthur laffer to describe revenue from taxes in terms of the tax rate. a function that might describe the entire laffer curve is given by y = x(100 - x)(x² + 400), where y is government revenue in hundreds of thousands of dollars from a tax rate of x percent, with the function valid for 0 ≤ x ≤ 100. find the revenue from the following tax rates. (a) 10% (b) 30% (c) 50% (d) 80% (e) graph the function. (a) the revenue from a tax rate of 10% is billion dollars. (simplify your answer.)

Answer

Explanation:

Step1: Substitute x = 10 into the function

Given $y=x(100 - x)(x^{2}+400)$, substitute $x = 10$: $y=10\times(100 - 10)\times(10^{2}+400)$

Step2: Calculate the values inside parentheses

First, $100 - 10=90$ and $10^{2}+400=100 + 400=500$. So $y=10\times90\times500$.

Step3: Perform the multiplications

$10\times90 = 900$, then $900\times500=450000$. Since $y$ is in hundreds of thousands of dollars, the value of $y$ in thousands of dollars is $450000\times100000 = 45000000000$ dollars or $4.5$ billion dollars.

Answer:

$4.5$