Question

4. There are 575 birds in an aviary. Each month, the number of birds decreases by 32. There are 350 trees in the aviary. Each month, 13 trees are added.Part A: Write functions to represent the number of birds and the number of trees in the aviary throughout the months. (4 points)Part B: How many birds are in the aviary after 3 months? How many trees are in the aviary after the same number of months? (2 points)Part C: After approximately how many months is the number of birds and the number of trees the same? Justify your answer mathematically. (4 points)(10 points)

Answer 1

A) B = 575 - 32m; T = 350 + 13m

B) 479 birds and 389 trees.

C) 5 months

Step-by-step explanation

Let the number of months be m.

Let the number of birds be B

Let the number of trees be T.

A) Initially there are 575 birds, but the number of birds decreases by 32 each month. This means that after m months, the number of birds is:

B = 575 - 32m

Initially there are 350 trees, but the number of trees increases by 13 each month. This means that after m months, the number of trees is:

T = 350 + 13m

B) After 3 months, m = 3.

This means that:

B = 575 - 32(3)

B = 575 - 96

B = 479 birds

This also means that:

T = 350 + 13(3)

T = 350 + 39

T = 389 trees

After 3 months there are 479 birds and 389 trees.

C) We want to find the number of months it will take the number of birds and trees to be equal. We have to equate B and T and find m:

575 - 32m = 350 + 13m

Collect like terms:

32m + 13m = 575 - 350

45m = 225

Divide both sides by 45:

m = 225 / 45

m = 5 months

It will take 5 months.