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3 years ago

On a piece of paper, graph y=4x-2. then determine which answer matches the graph you drew?

Mathematics

1 answer:

Natalka [10]3 years ago

3 0

Because this equation is in slope-intercept form, we can tell exactly how it will look by checking out 3 key points.

Leading coefficient: negative, or positive.

In this case, the leading coefficient is positive, which means that the slope will be going from bottom left to upper right.

Leading coefficient = slope

In this case, the slope is 4, or 4/1, so it will be at a steep incline.

Value of constant = y-intercept.

In this case, the y-intercept is -2, which will help us narrow down our choice.

<h3><u>After reviewing the three answer choices, the most likely selection will be A, as it seems to have a slope of 4, it is positive, and it has a y-intercept of -2.</u></h3>

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Assume the exponential growth model A(t)equals=Upper A 0 e Superscript ktA0ekt and a world population of 5.95.9 billion in 2006

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Answer:

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Step-by-step explanation:

We are given the following in the question:

The exponential growth model is given by:

$A(t) = A_0e^{kt}$

where k is the growth rate, t is time in years and $A_0$ is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

$A_0 = 5.9\text{ billions}$

We have to find the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Putting these values in the growth model, we have,

$24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%$

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

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