so p(0)=(234.375)(1)=234.375
so The Initial Population is 234.375, but we cant have 0.375 of a person lol, so just round it to 234
Answer Initial population=234
Second part:(Yay)
the size of the bacteria after 3 hours.
we know the initial population.
First we convert 3 hours to minutes-->60 minutes in an hour, but we have 3 hours so multiply 60 3 times to get 60*3=180 minutes in 3 hours yay!
Now put in formula(You can use our simplified one that doesnt involve the "e and ln"
to get p(180)=(234.375)(2)^(180/10)
=(234.375)(2^18)=61440000
So the population after 3 hours is->61440000
Optional:A proof and a mental picture
Just to have more understanding here is another way to precieve the second question:
Since they told us that the population doubles every 10 minutes alll we need to do is break the 180 minutes in chunks of 10 minutes so we can have an easy understandings yay!
So divide 180 by 10 to get 180/10=18
There are 18, 10 minutes in 3 hours yay and since the intial population is 234.375
just multiply the 234.375 poulation doubles 18 times
so, lets do it just to verify our answr(Yay)
234.375*2*2*2*2*2*2*2*2*2*
2*2*2*2*2*2*2*2*2=61440000 we ARE CORRECT
* I hope I helped make this fun with all the "Yays" rather than annoying lol