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PRACTICE Emmanuel is growing a plant for a science experiment. Each day, he records the height of the plant...

10. PRACTICE Emmanuel is growing a plant for a science experiment. Each day, he records the height of the plant in centimeters. His data for the first few days are shown in the table.
Time (days) | Height (cm)
0 | 1.3
1 | 2.0
2 | 2.7
3 | 3.4
a. Extend the table to predict the height of the plant after 7 days.
Time (days) | Height (cm)
0 | 1.3
1 | 2.0
2 | 2.7
3 | 3.4
b. Is the relationship between the time and the height of the plant a function?
11. PRACTICE Write your own example of a function. What is the independent variable?

Answer

10a. The height increases by 0.7 cm each day, so h = 1.3 + 0.7t. Extend the table with:

  1. Day 4: 4.1 cm
  2. Day 5: 4.8 cm
  3. Day 6: 5.5 cm
  4. Day 7: 6.2 cm

The predicted height after 7 days is 6.2 cm.

10b. Yes. Each time corresponds to exactly one plant height, so the relationship is a function.

11. Example: C = 3n gives the total cost C in dollars for n notebooks costing $3 each. The independent variable is n, the number of notebooks. The dependent variable is C, the total cost.

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