Algebra 2. Unit S03.Mathematical investigation
Round your answers to the nearest hundredths when needed.
The number of bacteria in some population can be described by the function
𝑨𝑨(𝒕𝒕) = 𝟐𝟐𝒆𝒆𝟎𝟎.𝟑𝟑𝟑𝟑
where 𝐴𝐴(𝑡𝑡) is the number of bacteria at time 𝑡𝑡,and time is measured in days.
Answer the following questions:
1)
Find the initial number of bacteria in this population.
2)
Graph the function 𝐴𝐴(𝑡𝑡) by point-plotting using 5 points with 𝒕𝒕 = 𝟎𝟎, 𝟏𝟏, 𝟑𝟑, 𝟓𝟓, 𝟔𝟔.
3)
4)
5)
6)
Find the appropriate domain of the function 𝐴𝐴(𝑡𝑡).
Find the appropriate range of the function 𝐴𝐴(𝑡𝑡).
Find the intercepts of the graph of A(t) and interpret them.
7)
Find the asymptotes of the graph of 𝐴𝐴(𝑡𝑡).
8)
Find the amount of population after 10 days.
9)
At what time the number of bacteria will reach 10,000?
10)
Find the amount of population after 18 hours.
Another population is described by the function
where time 𝑡𝑡 is measured in days.
𝑩𝑩(𝒕𝒕) = 𝟏𝟏𝟏𝟏𝒆𝒆𝟎𝟎.𝟏𝟏𝟏𝟏
At what time the number of bacteria in the two populations will be equal? What is the number
of bacteria in each population at that time?
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