Science:Math Exam Resources/Courses/MATH100 C/December 2024/Question 12 (a)/Solution 1

If someone with an income of $x=1$ (i.e., $10,000) earns one additional dollar, then the amount of tax they pay increases by approximately $\frac{5}{9}$ of a dollar.

In other words, $T^{\prime }(1)=\frac{5}{9}$ represents the marginal tax rate at an income of $10,000: for each extra dollar earned, about $\frac{5}{9}$ dollars is paid in taxes.