Cracking The Ap Calculus ab Exam 2018

This gives us G = 100ekt.

Next, we use the condition that G = 120 at time t = 1 to solve for k.

120 =   100ek

1.2 =   ek

ln  1.2 =   k   ≈   0.1823

This gives us G = 100e0.1823t.

(b) In how many years will the amount of grass available be 300 tons?

All we need to do is set G equal to 300 and solve for t.

300 =   100e0.1823t

3   =   e0.1823t

ln  3   =   0.1823t

t   ≈   6.026   years

(c) If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass,
how long will it take for the lake to be completely free of sea grass?

Now we have to account for the fish’s consumption of the sea grass. So we have to evaluate the

differential    equation        =   kG  −   80.

First, separate the variables, to get

    =   dt

Now, integrate both sides.

ln  =   kt  +   C

Next, exponentiate both sides to the base e. We get