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Ten blackberry plants start growing in my yard. Absent constraint, blackberries will spread by 200% a month. My yard can only sustain about 50 plants. Using the logistic growth model, a. Write a recursive formula for the number of blackberry plants in my yard b. Calculate the number of plants after 1, 2, and 3 months

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MrRoyal

The recursive formula for the number of blackberry plants in my yard is Tn = 3Tn-1 where To = 10

The recursive function

The given parameters are:

  • Initial = 10
  • Maximum = 50
  • Growth rate = 200%

The number of plants in month n is calculated using:

Tn = Tn-1 * (1 + 200%)

This gives

Tn = 3Tn-1

Hence, the recursive formula for the number of blackberry plants in my yard is Tn = 3Tn-1 where To = 10

The number of plants after 1, 2, and 3 months

This means that n = 1, 2, 3

When n = 1, we have:

T1 = 3To = 3 * 10 = 30

When n = 2, we have:

T2 = 3T1 = 3 * 30 = 90

90 is greater than the maximum number of plant the backyard can contain

Hence, the number of plants after 1 month is 30 and the plants in the backyard would exceed 50 plants before the end of the 2 months

Read more about recursive formulas at:

https://brainly.com/question/1275192

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