Let's break down the problem step by step.

a) Calculate the tax on $125,000:

• The first $50,000 is taxed at 5%.
• The remaining income above $50,000 is taxed at 12%.

1. For the first $50,000: $\text{Tax on } 50,000 = 50,000 \times 0.05 = 2,500$

2. For the income above $50,000, which is $125,000 - $50,000 = $75,000: $\text{Tax on } 75,000 = 75,000 \times 0.12 = 9,000$

3. Total tax: $\text{Total tax} = 2,500 + 9,000 = 11,500$

Thus, the total tax on $125,000 is $11,500.

b) Write a function that models the tax policy:

Let $T(x)$ be the tax on an income $x$.

• If $x \leq 50,000$, the tax is 5% of $x$: $T(x) = 0.05x \quad \text{for} \quad 0 \leq x \leq 50,000$

• If $x > 50,000$, the tax is 5% on the first $50,000 and 12% on the amount exceeding $50,000: $T(x) = 0.05 \times 50,000 + 0.12 \times (x - 50,000) = 2,500 + 0.12 \times (x - 50,000) \quad \text{for} \quad x > 50,000$

So the tax function $T(x)$ is: