There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed.

Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points)

Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points)

Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)

Question

03-05-2018
Mathematics

contestada

There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed.

Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points)

Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points)

Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)

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SkyCas SkyCas · Answer 1 · 2018-05-03T22:49:33+02:00

Part A: Since 85% of the marigold plants remain after each year, the equation for the marigold plants would be P=150(0.85)^x, with x being the amount of months. Since 8 sunflowers are removed from the initial 125 each month, then that equation would be P=125-8x, with x being the amount of months.

Part B: Just sub 3 in for the x in both equations, which will give you about 92 marigold plants left and 101 sunflower plants.

Part C: Enter both equations in to a scientific calculator and graph them. Then hit 2nd, trace, and 5 to find their intersection. The x-value of that intersection will be the number of years it takes for the amount of plants to be the same.