Question

Brett has been studying a type of bacteria that doubles every month. Originally, there were 5 bacterial cells. He wants to know how many there will be after 42 months. Which equation should he use?

A. a42 = 5(2)42 − 1

B. a42 = 5(2)(42)

C. a42 = 5(2)42

D. a42 = 5(2)(42 − 1)

Answer 1

At the very start, when no months have passed, we have 5 bacteria cells.
Let's call this \(\Large\rm a_0\), the amount \(\Large\rm a\).
The subscript 0 tells us how many months have passed.

After one month, \(\Large\rm a_1=5(2)\)
we double the 5.

After two months, \(\Large\rm a_2=5(2)^2\)
we double the 5, then we double again.

After n months have passed, \(\Large\rm a_n=5(2)^n\)
we double n consecutive number of times.

So what about after 42 months,
what form do you think it will have? :)
Pssst! Plug in 42 for n.