Question

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)

Answer 1

For the marigolds
M = 150(0.85)^x where x is the number of months
For sunflowers
S = 125 - 8x where x = number of months

Part B
after 3 months there are 150(0.85)^3 = 92 marigolds

after 3 moths there are 123 - 8*3 = 99 sunflowers

Part C

There are the same number of plants when the 2 functions are equal:-

So we have 150(0.85)^x = 125 - 8x
solving this for x is not straight forward . it could be done by drawing 2 graphs and seeing where they intersect.

They come close to being equal after 2 months and after 14 months

Check out the graph on
www.desmos.com/calculator/i3m55hb2i3