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Ivan
3 years ago
11

Choose the function whose graph is given by:

Mathematics
2 answers:
xeze [42]3 years ago
6 0

Answer:

Option B. y = cosx + 1

Step-by-step explanation:

To understand the given graph we will note down it's features as below.

1). Since it's a periodic function and y value of graph is maximum at x=0 so its a cosine function.

2). Vertical shift of the graph is 1 means y=0 is the mid line of the graph.

3). Amplitude of the graph is = (2-0)/2 = 1

4). Phase shift of the given graph = 0

The graph satisfying all properties is option B. y = cosx + 1

Daniel [21]3 years ago
4 0

Answer:

The correct option is B.

Step-by-step explanation:

From the given graph it is clear that the maximum value of the function is 2 at x=0, so it a cosine function.

The general form of a cosine function is

y=a\cos(bx+c)+d       .... (1)

Where, a is amplitude, 2π/b is period, c is phase shift and d is midline.

Since maximum value is 2 and minimum value is 0, so

Amplitude=a=\frac{2-0}{2}=1

Midline=b=\frac{2+0}{2}=1

Period=2\pi\Rightarrow b=1

Since maximum value is at x=0, therefore the phase shift is c=0.

Put these values in equation 1.

y=1\cos(1x+0)+1

y=\cos(x)+1

Therefore the correct option is B.

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Answer:

(a) n(t) = P(0)*e^(0.010939940t)

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Step-by-step explanation:

rate = 1.1% / year = 1.011

(a)

P(0) = 12,000,000  = population in 2010

In compound interest format, after t years

P(t) = P(0)* (1.011)^t

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therefore

e^(rt) = 1.011^t       use law of exponents

(e^r)^t = 1.011^t

e^r = 1.011

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n(t) = P(0)*e^(0.010939940t)

(b)

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to reach 14 million, we equate

n(t) = 14,000,000

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0.010939940*t = log(7/6)

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See graph attached.  Y-axis is in millions, x-axis is in years.

4 0
3 years ago
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