That is because mass and volume depend on the size of the sample. The same substance can come in different sizes in which its mass and volume would be different.
Answer:
Hey there!
We have an=a1(r^n-1), which is the formula for a geometric sequence.
The common ratio is 3, and 2 is the 1st term.
Thus, we have a1=2(3)^(n-1)
Hope this helps :)
a. Salt flows into tank A at a rate of
(<em>y</em>(<em>t</em>)/500 lb/gal) * (50 gal/min) = <em>y</em>(<em>t</em>)/10 lb/gal
and out at a rate of
(<em>x</em>(<em>t</em>)/500 lb/gal) * (50 gal/min) = <em>x</em>(<em>t</em>)/10 lb/gal
so the net rate of change of the amount of salt in tank A is
Similarly, you would find
b. We have
Notice that <em>x'</em> = -<em>y'</em>, so
Solve for <em>x</em>: the characteristic equation
has roots and , so
Again using the fact that <em>y'</em> = -<em>x'</em>, we then find
Given that <em>x</em>(0) = 0 and <em>y</em>(0) = 10, we find
The number of ants in a colony doubles every 8 weeks.
Constant rate of change means that when the value of x increases, the y remains constant. So there is no change in the y value. In this case, the x value is the "week" and the y value is the "amount of ants".