Which of the following is true for f(x) = –2sin(x) – 3?
1 answer:
Answer: Option C is correct!
Step-by-step explanation:
The range of function is [-1,-5] . so first option is incorrect.
Since graph of the function f(x)=-2sin(x) is shifted down by 3 because of -3
therefore option B is incorrect.
Period of the given function is 2pi because here b =1 and period of sinx function is given by therefore option D is also incorrect
Period of the function f(x) is always absolute value number in front of sinx which is given to be 2 here therefore option C is correct.!
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Option a: The number of bacteria at time x is 0.
Option b: An exponential function that represents the population is
Option c: The population after 10 minutes is 11534(app)
Explanation:
It is given that the coordinates of the graph are (0,200), (1,300) and (2, 450)
Option a: To determine the number of bacteria x when y = 200
From the graph, we can see that the line meets y = 200 when x = 0
Thus, the coordinates are (0,200)
Hence, the number of bacteria at time x is 0 when y = 200.
Option b: Now, we shall determine the exponential function of the population.
The general formula for exponential function is
Where a is the starting point and
b is the common difference.
To determine the common difference, let us divide,
Also,
Hence, the common difference is
Thus, substituting the values and
in the formula
,
we have,
Hence, An exponential function that represents the population is
Option c: To determine the population after 10 minutes, let us substitute in
, since the x represents the population of the bacteria in minutes.
Thus, we have,
Hence, the population after 10 minutes is 11534(app)