Answer:
After 16 months, Kenya will have paid $5,550
Step-by-step explanation:
This is a guess and check type of a problem. You guess a number of months, plug it into x, and see if both equations come out with the same answer.
If you plug 16 into the first dealer's equation, you get y= 200(16) + 2350. Solving this equation will mean y equals 5550.
If you plug 16 into the second dealer's equation, you get y= 175(16) + 2750.
Solving this equation will mean y also equals 5550.
T = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120
Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10
Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)
0 = 3t - 2
2 = 3t
2/3 = t
Plug 2/3 into original equation, this is a maximum. We want the minimum:
0 = t - 5
5 = t
Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5
