Question 1170427
Let's break down each part of the problem.

**(b) Immunization Costs**

We are given the cost function:
$$C(x) = \frac{1.85x}{100-x}$$
where $x$ is the percentage of the susceptible population immunized, and $C(x)$ is in million dollars.

**(i) Cost for the first 20%:**

We need to find $C(20)$.
$$C(20) = \frac{1.85(20)}{100-20} = \frac{37}{80} = 0.4625$$
So, it would cost 0.4625 million dollars, or $462,500.

**(ii) Cost for the next 30%:**

If we immunize the first 20%, then we need to immunize from 20% to 50%.
First, find the cost of immunizing 50%:
$$C(50) = \frac{1.85(50)}{100-50} = \frac{92.5}{50} = 1.85$$
The cost for the next 30% is $C(50) - C(20)$:
$$1.85 - 0.4625 = 1.3875$$
So, it would cost 1.3875 million dollars, or $1,387,500.

**(iii) Percentage not immunized with $17 million:**

We need to find $x$ such that $C(x) = 17$:
$$17 = \frac{1.85x}{100-x}$$
$$17(100-x) = 1.85x$$
$$1700 - 17x = 1.85x$$
$$1700 = 18.85x$$
$$x = \frac{1700}{18.85} \approx 90.1856764$$
So, approximately 90.19% of the population can be immunized.
The percentage not immunized is $100 - x$:
$$100 - 90.19 \approx 9.81$$
Approximately 9.81% of the population will not receive immunization.

**(iv) Immunization for the entire population:**

If we want to immunize 100% of the population, we need to find $C(100)$:
$$C(100) = \frac{1.85(100)}{100-100} = \frac{185}{0}$$
This is undefined, as we cannot divide by zero.
Therefore, it is impossible to immunize the entire susceptible population.

**(c) Discontinuity of f(x)**

You didn't provide the function f(x). However, I can explain how to find the discontinuities of a function.

**Finding Discontinuities:**

* **Rational Functions:** If $f(x)$ is a rational function (a fraction where the numerator and denominator are polynomials), then the function is discontinuous where the denominator is zero.
* **Piecewise Functions:** If $f(x)$ is a piecewise function, then the function is discontinuous where the pieces do not meet.
* **Other Functions:** If $f(x)$ involves other functions like logarithms or square roots, then the function is discontinuous where those functions are undefined.

**Example:**

Let's say $f(x) = \frac{x+1}{x-2}$.

To find the discontinuities, we set the denominator to zero:
$x - 2 = 0$
$x = 2$

Therefore, $f(x)$ is discontinuous at $x = 2$.

**Please provide the function f(x) so I can determine its discontinuities.**