Exponential Growth and Decay Models
Key Questions

Answer:
Population
#[P]= Ce^[kt# Explanation:
If the rate of growth
#P# is proportional to itself, then with respect to time#t# ,#[dP]/dt=kP# , ....inverting both sides, .....#dt/[dP]=[1]/[kP# and so integrating both sides#intdt=int[dP]/[kP# , thus,.....#t=1/klnP +# a constant............#[1]# Suppose
#P# is some value# C# when# t=0# , substituting#0=1/klnC+# constant, therefore the constant#= 1/klnC# and so substituting this value for the constant in ...#[1]# we have ,#t= 1/k[ln PlnC]# =#1/k ln[P/C]# , therefore ,#kt=ln[p/C]# [ theory of logs] and so#e^[kt]=P/C# ......giving# P=Ce^[kt# . The constant#k# will represent the excess of births over deaths or vice versa for a decreasing rate.
Questions
Applications of Definite Integrals

Solving Separable Differential Equations

Slope Fields

Exponential Growth and Decay Models

Logistic Growth Models

Net Change: Motion on a Line

Determining the Surface Area of a Solid of Revolution

Determining the Length of a Curve

Determining the Volume of a Solid of Revolution

Determining Work and Fluid Force

The Average Value of a Function