To solve this problem, let us first assign variables. Let
us say that:
X = number of marigold plants
Y = number of sunflower plants
n = number of months
We can see that in the given problem, X is decreasing by
a percentage, this means that we have to set-up a geometric equation while for Y
the decrease is linear so we set-up an arithmetic equation.
Part A.
For marigold plants X, a geometric sequence has a general
form of:
X = Xo * (1 + r)^n
where r = -15% = -0.15 (negative
since it is decreasing)
Xo = the initial amount of marigold plants = 150
X = 150 * (1 – 0.15)^n
X = 150 (0.85)^n
For the sunflower plants Y, an arithmetic sequence has a
general form of:
Y = Yo + d * n
where d = -8 and Yo = 125
Y = 125 – 8 n
Part B. For n = 3
X = 150 (0.85)^3 = 92.12 = 92
Y = 125 – 8 (3) = 101
Part C. From Part B we see that the two values are very
far from each other when n = 3, therefore they must be similar when n < 3.
So we try n = 2
X = 150 (0.85)^2 = 108.38 = 108
Y = 125 – 8 (2) = 109
Therefore the two plants have approximately similar
amount after 2 months.
