Answer
(a)$Q(5)\approx2.719 lbs$
(b)$Q(10)\approx4.945 lbs$
(c) See the image below.
(d) as $t$ becomes infinitely large, the amount of salt in the barrel approaches $15$.
$50gal \times 0.3lb/gal=15lb$ (This concentration can in $50gal$ barrel can have $15lbs$ salt at most).
Work Step by Step
We have a function $Q(t)=15(1-e^{-0.04t})$ which represents the amount of salt $Q(t)$ (pounds) for given $t$ minutes.
(a) $t=5$
$Q(5)=15(1-e^{-0.04\times5})=15(1-e^{-0.2})=15(1-\frac{1}{e^{0.2}})=15-\frac{15}{e^{0.2}}\approx2.719 lbs$
(b) $t=10$
$Q(10)=15(1-e^{-0.04\times10})=15(1-e^{-0.4})=15(1-\frac{1}{e^{0.4}})=15-\frac{15}{e^{0.4}}\approx4.945 lbs$
(c) See the image above.
(d) as $t$ becomes infinitely large, the amount of salt in the barrel approaches $15$.
This was expectable, because we have a limited space and the concentration of the salt water pumped into the barrel is constant. As we are not putting any extra salt into the barrel the concentration stays the same and can get at most:
$50gal \times 0.3lb/gal=15lb$
