Not sure how to do this

Question

The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours, there are 100 bacteria, and after 5 hours, there are 800 bacteria. How many bacteria will there be after 6 hours?

Answer 1

B = Bo(e^rt)

100=Boe^2r

800=Boe^5r

8 = e^3r

ln8 = 3r

r = ln8/3 =about .69315

100=Boe^.69315(2)

Bo = Beginning Bacteria = 100/e^1.363 = 25.59 orignally

in 6 hours

B = Bo(e^rt)

B = 25.59e^.69315(6) = about 1,638

but that's got some rounding errors which compound in the calculations

originally 25

in one hour it doubles to 50

2 hours doubles again to 100

3 hours 200

4 hours 400

5 hours 800

6 hours 1600