To get started, we will use the general formula for bacteria growth/decay problems:
where:
A_{f} = Final amount
A_{i} = Initial amount
k = growth rate constant
t = time
For doubling problems, the general formula can be shortened to:
Now, we can use the shortened formula to calculate the growth rate constant of both bacteria:
Colby (1):
per hour
Jaquan (2):
per hour
Using Colby's rate constant, we can use the general formula to calculate for Colby's final amount after 1 day (24 hours).
Note: All units must be constant, so convert day to hours.
Remember that the final amount for both bacteria must be the same after 24 hours. Again, using the general formula, we can calculate the initial amount of bacteria that Jaquan needs:
where:
A_{f} = Final amount
A_{i} = Initial amount
k = growth rate constant
t = time
For doubling problems, the general formula can be shortened to:
Now, we can use the shortened formula to calculate the growth rate constant of both bacteria:
Colby (1):
Jaquan (2):
Using Colby's rate constant, we can use the general formula to calculate for Colby's final amount after 1 day (24 hours).
Note: All units must be constant, so convert day to hours.
Remember that the final amount for both bacteria must be the same after 24 hours. Again, using the general formula, we can calculate the initial amount of bacteria that Jaquan needs: