Look at the tables and answer the questions.

Question

Find an equation of the form  that fits the data below

x	0	1	2	3
y	5	33	180	1077

To fit the data:

a =

b =

c =

Find a possible formula for the trigonometric function whose values are in the following table.

x	0	2	4	6	8	10	12
y	-1	3	7	3	-1	3	7

Y=

Answer 1

For the first problem, just plug in the values of x & y from the data points to solve for a, b, and c.

First plug in x = 0, y = 5 to get:

5 = ab⁰ + c(sin(π/2•0))

5 = a(1) + c(0)

a = 5

Then plug in x = 2, y = 180 to get:

180 = 5(b²) + c(sin(π/2•2))

180 = 5b² + 0

b² = 36

b = 6

Then plug in x = 1 y = 33 to get:

33 = 5•6¹ + c(sin(π/2•1))

33 = 30 + c(1)

c = 3

For the second problem, The maximums are both at 3 and the minimums are both at -1 and they are all equal spacing so a sine function would work nicely. The midline is the average between the max and min so (3 + -1)/2 = 1 and the amplitude is 2. The period is 4 (distance between a max and the next max.

Since the function starts at zero at the minimum, it would be easiest to use a negative cosine to model this. So:

y = -2cos(2π/4) + 1 or (simplifying)

y = -2cos(π/2) + 1