Suppose that 40 deer are introduced in a protected wilderness area. The population of the herd P can be approximated by P = 40 + 20 x 1 + 0.05 x r where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.
Suppose that 40 deer are introduced in a protected wilderness area. The population of the herd P can be approximated by P = 40 + 20 x 1 + 0.05 x r where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.
Solution Summary: The author calculates the time required for the population of the herd, P, when 40 deer were introduced in a protected wilderness area.
Suppose that 40 deer are introduced in a protected wilderness area. The population of the herd P can be approximated by
P
=
40
+
20
x
1
+
0.05
x
r
where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.
A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?
College Algebra with Modeling & Visualization (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY