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INTERPOLATION & EXTRAPOLATIONA student in electronics measured the current through a circuit with a constant resistance while the voltage was increased. The results are shown below, with the voltage measured in volts and the current in milliamps.

a) Make a scatterplot of the data. Set the window to show the origin (0, 0) and the x-and y-axes.

f) What would be the current if the voltage were 22.736 volts?

e) What would be the current if the voltage were 8.000 volts?

d) What is the slope of the line?

c) Rewrite the equation, using the voltage as, V, and the current as, I.

b) What is the equation for a line of best fit? (Use three decimal places)

INTERPOLATIONEXTRAPOLATION

HOMEWORK

INTERPOLATION & EXTRAPOLATION

a) Make a scatterplot of the data. Set the window to show the origin (0, 0) and the x-and y-axes.

d) What is the slope of the line?

c) Rewrite the equation, using the voltage as, V, and the current as, I.

b) What is the equation for a line of best fit? (Use three decimal places)

INTERPOLATION & EXTRAPOLATION

f) What would be the current if the voltage were 22.736 volts?

e) What would be the current if the voltage were 8.000 volts?

EXTRAPOLATION

INTERPOLATION

22.736 22.736

In an experiment, the following masses were attached to a spring. As they were attached, the following elongations were recorded:1. What is the independent variable?

6. Do you think that this model for the elongation of the spring is always accurate? What do you think would happen if the mass were increases to 15 kg?

5. Is it the same in the equation of the line?

4. Select two points in the table and use them to calculate the slope of the line.

3. Use your calculator to find a regression line (line of best fit) for the data. What is the y-intercept?

2. Use your graphing calculator to plot the elongation against mass.

HOMEWORK

Jimmy has observed that the distance to a thunderstorm can be estimated by counting the number of seconds between a flash of lightning and the sound of the thunder. With further investigation, he obtains the following information:

a. Complete the pattern shown in the chart up to 21 seconds.

b. Graph the information using t as the independent variable and d as the dependent variable.

c. What is the equation for this direct proportion? What is the constant of proportionality? This can be calculated in the same way as the slope of a line.

d. Estimate the distance if the time is 10 seconds, 20 seconds, 30 seconds.

Find the next three terms in each sequence of numbers ...

1, 1, 2, 3, 5, 8,13, , ,

3, 6, 12, 24, , ,

32, 16, 8, 4, , ,

4, 7, 10, 13, , ,

4, 7, 10, 13, , ,

Sequence: An ordered list of numbers that follow a certain pattern (or rule).

Arithmetic Sequence:(i) Recursive Definition: An ordered list of numbers generated by continuously adding a value (the common difference) to a given first term.(ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by a linear equation.

Some Definitions

Common Difference (d):(i) The number that is repeatedly added to successive terms in an arithmetic sequence.

(ii) From the implicit definition, d is the slope of the linear equation.

Example: Find the 51st term (t51) of the sequence 11, 5, -1, -7, ...

Solution: a = 11 t51 = 11 + (51 - 1)(-6)

d = 5 - 11 t51 = 11 + (50)(-6)

= -6 t51 = 11 - 300

n = 51 t51 = -289

tn is the nth terma is the first termn is the "rank" of the nth term in the sequenced is the common difference

tn = a + (n - 1)d

To Find the nth Term In an Arithmetic Sequence

d is the common difference

tn is an arbitrary term in the sequence

t(n - 1) is the term immediately before tn in the sequence

d = tn - t(n - 1)

To Find The Common Difference

Implicitly

Which of the following sequences are arithmetic sequences?

a) 1, 2, 6, 24, 120,…

b) 3, 9, 15, …

c) 2, 4, 8, 16, 32,…

d) 1, 2, 3, 5, 8, 13, …

e) -4, -1, 2, 5, 8,…

HOMEWORK

What is the pattern in the sequence 2, 8, 14, 20, 26…?Suggest an equation that could be used to generate such a list.

HOMEWORK

a) Why do the numbers 5, 8, 11, 14, 17… form an arithmetic sequence?

b) What is the defining equation that produced them?

c) What is the 27th term of this sequence?

HOMEWORK