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You plant a tomato plant in your garden. It starts at 8 inches tall. After 1 week, it grows to 11 inches tall. After two weeks, it is now 14 inches tall. After 3 weeks, the plant is 17 inches tall. Write a linear equation that represents this model. How tall is the tomato plant after 56 weeks?

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olya27

Answer:

The tomato plant is 176 inch tall after 56 weeks.

Step-by-step explanation:

x  ⇒ weeks and y ⇒ inch.

Week 0 the tomato plant starts at 8 inch tall, week 1 it grows to 11 inch tall, week 2 it grows to 14 inch tall, week 3 it grows to 17 inch tall, week 56 is ? inch tall. So, every week (x) the tomato plant grows 3 inch (y).

y = 3x + 8

y = (3 × 56) + 8  

y = 168 + 8

y = 176 inch
  • The linear function that represents the height of the plant after n weeks is:

[tex]h(n) = 8 + 3n[/tex]

  • Using the function, after 56 weeks, the height of the plant is of 176 feet.

The linear model for the height after n weeks has the following format:

[tex]h(n) = h(0) + an[/tex]

In which:

  • h(0) is the initial height.
  • a is the rate of change.

Starts at 8 inches tall, thus h(0) = 8. Each week the height increases 3 inches, thus, a = 3, and the model is:

[tex]h(n) = 8 + 3n[/tex]

After 56 weeks, the height is of h(56), thus:

[tex]h(56) = 8 + 3(56) = 176[/tex]

176 inches tall after 56 weeks.

A similar problem is given at https://brainly.com/question/16302622

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