The vertices of rectangle HIJK,after a reflection over the y-axis, are H′(–3, 6), I′(5, 6), J′(5, –1), and K′(–3, –1). What were
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Answer:
The correct answer is 54.76 years.
Step-by-step explanation:
The national health care expenditure (H) , in billion of dollars is modeled by
H = 29.57 × .
To measure the time before which national health expenditure reach 6000 billion dollars.
Thus putting the value of H = 6000 in the above modeled equation we get,
⇒ 6000 = 29.57 ×
⇒ =
⇒ 202.908 =
Taking logarithm with the base of e (㏑) both sides we get,
⇒ ㏑ 202.908 = ㏑
⇒ ㏑ 202.908 = 0.0970 × t
⇒ 0.0970 × t = 5.312
⇒ t =
⇒ t = 54.76.
Thus the total time required before which national health expenditure reach 6000 billion dollars is 54.76 years.
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)