本题目来源于试卷: IB MAI HL Functions Topic 2.4 Transformations,类别为 IB数学
[问答题]
A scientist is studying the growth of hgpp 0)ll 8n3la population of bacteria un *mjiw.o -vtw/der different enviro/om*i. wtvj -wnments. In environment A bacteria grows according to the function
$G(t)=−700(0.95)^t$+750
where G is the population of bacteria and t is the time in minutes since placed in the environment.
1.Find the initial population of bacteria.
2.Sketch a graph of G against t for 0≤t≤800.
3.Find the population of bacteria after 20 minutes.
4.Find the steady-state population of bacteria after a long period of time.
To slow down the growth of bacteria, the scientist creates a new environment, B, by reducing the pH level of the environment. The scientist finds that the bacteria now grow half as fast as in environment A.
5.Determine a model for the growth of bacteria $G_2$ for this modified environment.
The scientist creates a another environment, C, which is rich in proteins. The scientist finds that the bacteria grows twice as fast as in the original environment, A.
6.Determine a model for the growth, $G_3$, of bacteria in this protein-rich environment.
7.Find out how long it takes for the population of bacteria to reach 600 in environment C.
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