A tank contains 100 gal of water and 50 oz of salt. Water containing a salt concentration of 14(1+12 sint)oz/gal flows into the tank at a rate of 2 gal/min, and the mixture in the tank flows out at the same rate.(a) Find the amount of salt in the tank at any time.(b) Plot the solution for a time period long enough so that you see the ultimate behavior of the graph.(c) The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation?

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

47 - 90 = 43

43 - 180 = x

x = 137