We can call the moment when the scientist found the 24 bacteria x=0.
After one hour (x=1) there will be 48 bacteria, since they duble each hour.
After two hours (x=2) there will be 96 bacteria.
After three hours (x=3) there will be 192 bacteria.
We can rewrite these numbers as follows:
[tex]24=24\cdot1=24\cdot2^0[/tex][tex]48=24\cdot2=24\cdot2^1[/tex][tex]96=24\cdot4=24\cdot2^2[/tex][tex]192=24\cdot8=24\cdot2^3[/tex]
Thus, the best model for this behaviour is
[tex]y=24(2)^x^{}[/tex]
