Let
us first assign variables. We 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.
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