Q1 b) The quantity of liquid will stabilise when 10% of the amount Vn used in the afternoons becomes equal to 2000 liters added in the evenings.
(I think I'm posting in the right place, but not completely sure)
Question 1
The water used in the orchard is stored in a tank.
Each afternoon, 10% of the volume of water in the tank is used.
Each evening, 2 000 litres of water is added to the tank.
This pattern continues each day.
The volume of water, Vn , in the tank on the morning of the nth day is modelled by the difference equation
Vn + 1 = rVn + d where V1 = 45 000 litres.
a. Find r and d.
r =0.9
d =2000
b. In the long term, how many litres of water will be in the tank each morning?
Write your answer correct to the nearest litre
Question 2
A healthy eating and gym program is designed to help football recruits build body weight over an extended period of time. Rob, a new recruit who initially weighs 73.4 kg, decides to follow the program.
In the ﬁrst week he gains 400 g in body weight.
In the second week he gains 380 g in body weight.
In the third week he gains 361 g in body weight.
If Rob continues to follow this program indeﬁnitely, and this pattern of weight gain remains the same, his eventual body weight will be closest to
A. 74.5 kg
B. 77.1 kg
C. 77.3 kg
D. 80.0 kg
E. 81.4 kg
I tried S(infinity)=a/(1-r) But it can up with some crazy answer which couldn't be right.
Any help would be greatly appriciated.
Q2.
If the pattern goes like this
+400
+(400-20)
+(400-(20+19))
+(400-(20+19+18))+...
.
.
+(400-(20+19+18+...+1))
Then after 21 weeks the mass gained weekly would remain constant 400-(20*21)/2=190g, and after that every week he would put on additional 190g so he
continues with this program indefinitely he'd explode?
Am I mistaking somewhere?
Not sure if this helps - we may both be wrong!Code:week Gain(g) 1 400 2 380 20 3 361 19 4 343 18 5 326 17 6 310 16 7 295 15 8 281 14 9 268 13 10 256 12 11 245 11 12 235 10 13 226 9 14 218 8 15 211 7 16 205 6 17 200 5 18 196 4 19 193 3 20 191 2 21 190 1 22 190 0