Respuesta :
Answer:
1)
t=5 hours.
2)
40960 cells.
Step-by-step explanation:
A scientist studying bacteria begins with 20 cells.
The bacteria population doubles every hour.
Let P(t) determines the population of the bacteria in 't' hours.
Hence, by the given information our function P(t) is modeled as:
[tex]P(t)=20\times 2^t[/tex]
Now, we have to find the value of 't' such that:
P(t)>500
i.e.
[tex]20\times 2^t>500\\\\\\2^t>\dfrac{500}{20}\\\\2^t>25[/tex]
on taking logarithmic function on both side we get:
[tex]t\log 2>\log 25\\\\t>\dfrac{\log 25}{\log 2}\\\\t>4.64[/tex]
i.e. after 5 hours the population of the bacteria will exceed 500.
Now we have to find the value of function P(t) when t=11.
i.e.
[tex]P(11)=20\times 2^{11}\\\\P(11)=20\times 2048\\\\P(11)=40960[/tex]
Hence , the population of bacteria after 11 hours is:
40960 cells.
