### Home > APCALC > Chapter 7 > Lesson 7.4.1 > Problem7-183

7-183.

Etube is tending to the orange trees on his lot. Unfortunately, the trees are becoming infected and dying. The rate at which the trees are being infected per month is given by $3\sqrt{N}$ where $N$ is the number of living trees.

1. If at $t = 0$ there are $3000$ living trees, set up the appropriate differential equation to represent the number of living trees $N$ as a function of $t$, where $t$ is measured in months.

The initial condition is not relevant, yet.

$\frac{dN}{dt}=-3{\sqrt{N}}$

2. Solve the initial value problem to determine the number of living trees after $t$ months.

Separate the variables so that all of the '$N$' variables are on one side of the equation and all of the '$t$' variables are on the other.
Then integrate both sides of the equation and solve for '$N$'. Use the initial condition to solve for $C$.

3. How many trees will be infected at $t = 5$ months?

Evaluate.