Answer: plan Y will produce more vehicles after 4 years.
Step-by-step explanation:
1) Plan Y: Increase vehicle production by 5% every year. It means that the rate of production is in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = (ar^n - 1)/(r - 1)
Where
n represents the number of term(years) in the sequence.
a represents the first term(number of vehicles in the present year) in the sequence.
r represents the common ratio.
From the information given,
a = 10000
r = 1 + 5/100 = 1.05
n = 4 years
Therefore, the sum of the vehicles produced in the first 4 years, S4 is
S4 = (10000 × 1.05^(4) - 1)/1.05 - 1
S4 = (10000 × 0.21550625)/0.05
S4 = 2155.0625/0.05
S4 = 43101 vehicles
2) Plan Z: Increase production by 300 vehicles every year. It means that the rate of production is in geometric progression. The formula for determining the sum of n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
From the information given,
n = 4 years
a = 10000
d = 300
Therefore, the sum of the first 4 terms, S4 would be
S4 = 4/2[10000 × 2 + (4 - 1)300]
S4 = 2[20000 + (3)300]
S4 = 2 × 20900
S4 = 41800 vehicles
