Exponential Model

• $y=C{e}^{kt}$
  • C: initial value
  • k: constant of proportionality (exp growth if >0, exp decay if <0)
  • t: amount of time (any unit of time)
• Solution to the differential equation $\frac{dy}{dt}=ky$

Solving

• Given one data point
  1. Plug in the initial amount and ordered pair $(t,y)$
  2. Solve for the $k$ value
  3. Solve for what the problem is asking
• Given two data points
  1. Plug both data points into their own equations
  2. Divide the equations by each other
  3. Solve for the $k$ value in the divided equation
  4. Solve for what the problem is asking