6.3 Exponential Growth and Decay

The rate of change of y is proportional to y.  Write a differential equation to model this statement.

•  

   $\frac{��}{��}=��$ 

  
  

•  $\frac{dy}{dt}=ky$  
  

•  $y=e^{kt}+C$  
  

•  $\frac{dy}{dt}=ky+C$  
  

Bacteria in a certain culture increase at a rate proportional to the number present. If the number of bacteria doubles in three hours, in how many hours will the number of bacteria triple?

• 3ln3/ln2

• 2ln3/ln2

• ln3/ln2

• ln(27/2)

• ln(9/2)

During a chemical reaction, the rate of change of the amount of the chemical remaining is proportional to the amount remaining. At time t=0, the amount of the chemical is 12 moles. At time t=4, the amount of the chemical is 4 moles. At what time t is the amount of the chemical 3 moles? (A mole is a unit of measure used in chemistry.)

• 0.058

• 0.061

• 0.167

• 0.693

• 8.318