Determine a polynomial function whose graph passes through the given points. 5: (0,-5); (1,-4) ; (-1,-9); (2,-3),

The interpolating polynomial is

.

Step-by-step explanation:

First, notice that we want to calculate the interpolating polynomial through the points (0,-5); (1,-4) ; (-1,-9); (2,-3). This means that we want to find a polynomial such that

, and .

We will have four equations, so our polynomial will be, at most, of degree 3. Let us write

The coordinates give us the following equations:

Notice that from the second equation we know that . Then, we obtained the linear system of equations

which is equivalent to

.

So, we have reduced our interpolation problem to solve a linear system of equations. Now, notice that if we add the first two equations of the system we obtain

that yields .

Then, our system becomes

which is equivalent to

.

Recall that now the first two equations are just the same, so we will use the first and third ones:

.

If we multiply the first one and add it to the second we get:

that yields .

Thus, substituting this value in the first equation:

which is equivalent to . Then, .

Summing up all our results we get that the interpolating polynomial is

.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%