There are 1500 bees in a colony. Each month, the number of bees decreases by 12%. There are 800 flowering plants in a garden. Ea
ch month, 25 flowering plants are removed.
PLEASE SHOW WORK!!
Part A: Write functions to represent the number of bees and the number of flowering plants throughout the months. (4 points)
Part B: How many bees are in the colony after 6 months? How many flowering plants are in the garden after the same number of months? (2 points)
Part C: After approximately how many months is the number of bees and the number of flowering plants the same? Justify your answer mathematically. (4 points)
PLEASE SHOW WORK!!
Part A: Write functions to represent the number of bees and the number of flowering plants throughout the months. (4 points)
Part B: How many bees are in the colony after 6 months? How many flowering plants are in the garden after the same number of months? (2 points)
Part C: After approximately how many months is the number of bees and the number of flowering plants the same? Justify your answer mathematically. (4 points)
1 answer:
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Answer:
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Answer:
10 years and 10 months.
Step-by-step explanation:
The annually interest rate (ia) can be converted by monthly (im) by the equation:
(1 + im)¹² = 1 + ia
(1 + im)¹² = 1 +0.01
(1 + im)¹² = 1.001 (putting ln in both sides)
ln(1 + im)¹² = ln1.001
12*ln(1 + im) = 1.0x10⁻³
ln(1 + im) = 8.33x10⁻⁵(applying "e in both sides)
1 + im = 1.00083
im = 0.00083 = 0.083%
For a investimenting, the final amount (A) can be calculated by:
Where R is the amount invested per month, i is the interest, and n the number of months:
160000 = 400 *
= 400
1.00083ⁿ - 1 = 0.332
1.00083ⁿ = 1.332 (applying ln in both sides)
n*ln1.00083 = ln1.332
8.3x10⁻⁴n = 0.2867
n = 345.4 months
345.4 months *1 yea12 months = 10 years and 10 months.