Ted invests $8,310 in a savings account with a fixed annual interest rate of 2% compounded continuously. How long will it take f
1 answer:
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Answer:
City @ 2017 = 8,920,800
Suburbs @ 2017 = 1, 897, 200
Step-by-step explanation:
Solution:
- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:
0.94*p_c + 0.04*p_s = p_c'
0.06*p_c + 0.96*p_s = p_s'
- Assuming 6% moved while remaining 94% remained settled at the time of migrations.
- The matrix representation is as follows:
- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:
- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:
- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.
- Where,
- The population in 2017 x_2 would be:
Answer:
a)
b)
Step-by-step explanation:
Data
Brine a (Ba)
Brine b (Bb)
we have that per every minute the amount of solution that enters the tank is the same as the one that leaves the tank (15 Lt / min)
, then the amount of salt (y) left in the tank after (t) minutes:
Finally:
a)
b)
being y(t) the amount of salt (y) per unit of time (t)