Video Transcript
A microorganism reproduces by
binary fission, where every hour each cell divides into two cells. Given that there were 15,141 cells
to begin with, determine how many cells there were after five hours.
Since this microorganism is
reproducing, we will expect more cells and not less, which means we’re expecting
exponential growth. Our unit of time is every hour. That means we can let 𝑡 be equal
to the hours after the initial count. If every hour one cell divides into
two cells, one cell becomes two cells in an hour. After an additional hour, the two
cells become four. This represents a doubling of the
cells every hour.
So we’ll need to take our
exponential form 𝑓 of 𝑥 equals 𝐴 times 𝑏 to the 𝑥 power, where 𝐴 is our
initial value, 15,141. 𝑏 is the rate. Since our rate is doubling, 𝑏 is
equal to two. And our variable will be 𝑡. It’ll be units of time. We now wanna take this function and
use it to solve for how many cells there were after five hours, which means we need
to calculate 15,141 times two to the fifth power, which is 484,512. After five hours, we can expect
that this microorganism will have 484,512 cells.
