Hello! Let's look at the two parts of this question.
Complete the table:
In this case, you just substitute the value of "hour" into the equation, for the value of t. For example:
P(0) = 120 [tex](2)^{0}[/tex]
P(0) = 120 (1)
P(0) = 120
Therefore, the number of bacteria for hour 0 is 120.
You can do this for the next ones. Hour 1 = 240, hour 2 = 480, and so on. (In this case, you can keep multiplying by 2)
Estimate when there will be more than 100,000 bacteria:
Set the final value of P(t) = 100,000, then solve.
100,000 = 120 (2[tex])^{t}[/tex]
833.33 = (2[tex])^{t}[/tex]
t = [tex]log_{2}833.33[/tex]
t = 9.702744108
So your answer would be around 9.7 years, or, around 10 years.
Hope this helps!
