Bacteria (help!)

Question

A starting sample of 5000 bacteria decreases in number by 25% per week.
Write the formula for an exponential function f(x)=Cax that models this situation.
What is C? What is a? What is x? What are their units?
Evaluate the result for how many bacteria are left after 4 weeks.
Show and discuss your work.

Answer 1

Use the formula

 

f(x) = Ca^x

 

f(x) = 5000(1 - 0.25)^x

 

f(x)= 5000(0.75)^x

 

where:

f(x) = the amount of bacteria after amount of weeks

C = initial amount of bacteria

a = growth factor

x = the time in weeks

 

So now evaluate f(4) to find the amount of bacteria after 4 weeks.