Question

X = 1/ 3 ( 1 − e -y )

Do not replace symbol e by its decimal approximation, do not
replace ordinary fractions by decimal fractions (for example, do
not replace 1/3 by 0.33).

Answer 1

The question covers solving exponential equations, using scientific notation and refining approximate solutions through successive approximation, as well as applying the power rule when dealing with cubing exponentials.

Step-by-step explanation:

The question involves various mathematical concepts such as solving equations with exponentials, understanding the scientific notation, and working with successive approximation methods. For example, when given y = 0.011, and you have improved the y value from 0.012 to 0.011, you substitute this new value of y into the given function to find a refined value of x. Through the process of refinement using a calculator, the value of x improves from 2.9 × 10-4 to a new value of 3.2 × 10-4. Additionally, the topic of cubing of exponentials is discussed where you cube the digit term normally, and multiply the exponent by 3, according to the power rule in exponents.