### All Algebra II Resources

## Example Questions

### Example Question #21 : Graphing Data

Given and use linear interpolation to find when .

**Possible Answers:**

**Correct answer:**

Use the formula for interpolation:

We will use (30, 15) as x2 and y2, (15, 10) as x1 and y1, and solve for y when x=17.9:

### Example Question #22 : Graphing Data

Mary measures her height every year on her birthday, starting at 11 until she turns 16. She wants to make a table with all the information gathered, but discovers she lost the piece of paper on which she wrote her height down on her 14^{th} birthday. Her incomplete table looks like this:

Age (years) | Height (inches) |

11 | 47.5 |

12 | 50.25 |

13 | 53 |

14 | ? |

15 | 58.5 |

16 | 61.25 |

Using the method of linear interpolation, which of the following is the *closest estimate* of Mary's height on her 14^{th} birthday?

**Possible Answers:**

Not enough information given in the problem.

**Correct answer:**

Using *linear interpolation* means that we draw a line between the points on our data set and use that line to estimate a value that lies *between *two data points; in this case, we have the data from Mary's 13^{th }and 15^{th} birthdays, so we can describe a line between those two points and estimate her height at 14. Our line will be written in *slope-intercept form:*

Where the variable represents Mary's Age in years and the variable represents her height in inches. First, we need to find the slope. Using 2 points on our table and as point 1 and point 2, respectively, we plug these values into our *slope formula*:

Next, we find the y-intercept by plugging in our slope (which we just found) and a point from our table (we'll stick with ) and solving for :

Simplify:

Subtract 35.75 from both sides to solve for :

The equation of our interpolation line is:

So, to get an estimate of Mary's height on her 14^{th} birthday, we plug in and solve for :

Our estimate of Mary's height at is

### Example Question #441 : Basic Statistics

Find the value of when given the points and .

**Possible Answers:**

**Correct answer:**

Write the interpolation formula.

Identify and substitute the values.

Simplify the fraction.

The answer is:

### Example Question #1 : Extrapolations

What is the next number in this sequence: 8, 27, 64, 125 ?

**Possible Answers:**

**Correct answer:**

Find the pattern of the sequence:

This pattern is so the next number in the sequence would be

### Example Question #1 : Extrapolations

Find the next 2 numbers in this sequence: 33, 46, 72, 111

**Possible Answers:**

**Correct answer:**

Find the pattern in this sequence of numbers:

In this case, the pattern is adding 13n to the previous number where n= how many numbers came before the current number.

so the first number we are looking for would be:

the second number we are looking for would be:

### Example Question #3 : Extrapolations

The amount of water inside of a leaky boat is measured periodically after the boat has been in the water in different periods of time and are found to have a linear relationship. The results are given in the following chart:

Time in water (mins) | Amount of water in the boat (gal) |

0 | 0 |

6 | 4.8 |

19 | 15.2 |

28 | 22.4 |

Using the method of linear extrapolation based on the data from the table, how much water would you expect to be in the boat after minutes?

**Possible Answers:**

**Correct answer:**

To extrapolate the results of the study out to 53 minutes, first we have to determine an equation representing the relationship between time passed and amount of water; we can write our equation in *slope-intercept form*:

Where our y-axis represents amount of water and the x-axis represents time. We can pick 2 points and label them *Point 1* and *Point 2*; looking back at the table:

Time in water (mins) | Amount of water in the boat (gal) |

0 | 0 |

6 | 4.8 |

19 | 15.2 |

28 | 22.4 |

We label *Point 1* as and *Point 2* as ; we plug these points into the slope formula as follows:

So, the slope of our line that describes how much water is in the boat is ; to find our term, the y-intercept, we need to pick a point on the graph and plug in our slope to solve for y-intercept. Let's once again choose the point :

Simplify the expression and we find that b=0, so our *slope-intercept* equation is:

Plugging in a value of 53 for , we find that:

So the answer is 42.4 gallons of water in the boat after 53 minutes.