Consider the following points.
(−1, 3), (0, 0), (1, 1), (4, 52)
(a) determine the polynomial function of least degree whose graph passes through the given points.
consider the following points.
(−2, 44), (−1, 0), (0, −14), (1, −16), (2, 0)
(a) determine the polynomial function of least degree whose graph passes through the given points.

a.

b.

Step-by-step explanation:

A polynomial of degree three satisfies the four points offered, in this way, if we evaluate said polynomial in the points, we can generate a linear system of four equations with four incognites that when solved will allow us to know the coefficients.

The linear system is:

The solution of the linear system is:

Then the function is:

b. A polynomial of degree four satisfies the five points offered, in this way, if we evaluate said polynomial in the points, we can generate a linear system of five equations with five incognites that when solved will allow us to know the coefficients.

The linear system is:

The solution of the linear system is:

Then the function is:

answer: 40.95

step-by-step explanation:

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: