The following function represents the value of a house after x years:

Mathematics

2 answers:

Natasha2012 [34]4 years ago

4 0

Answer: The decrease in the value of the house per year, which is 4%

Step-by-step explanation:

Hi, to answer this question we have to analyze the expression given:

F(x) = 242,000(0.96) x

F(x) represents the value of the house after x years

242,000 represent the actual value of the house

X represents the years

0.96 is affecting the present value of the house, and is a number smaller than 1, by 0.04(if we multiply 0.04 by 100 we obtain the percentage which is 4%).

So, it represents the decrease in the value of the house per year, which is 4%.

kakasveta [241]4 years ago

3 0

Hi there!

The answer is the decrease in the value of the house per year, which is 4%.

The present value of the house is represented by 242,000.

The value of the house after x years is represented by the entire function f(x) = 242,000(0.96)^x.

Hence, 0.96 represents the decrease in value per year (since it represents the factor of growth, and is smaller than 1, so we're dealing with a decrease), which is 4%.

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Yanka [14]

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10x + 10x + (6x + 8) + (6x + 8)
20x + 12x + 16 = P
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Now you just plug in x and finish the rest of the problem, and you have the answer:
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4 0

3 years ago

A slope field produces...

balandron [24]

It's A. B doesn't really make sense ("derivative of the differential equation" is somewhat nonsensical, "derivative of an equation" is not meaningful).

More to the point: Slope fields are used to visualize solutions to differential equations of the form

y' = f(x, y)

You take some point (x, y) and evaluate y' at the point. This gives the slope of the line tangent to the particular solution to the DE that passes through the point (x, y ).

Sample several points and evaluate y' at those points and you get several different slopes.

Simple example:

y' = x ² - y ² = (x + y ) (x - y )

Let's take the points (1, 1), (-1, 0), and (2, -2), at which we get slopes

y' = f (1, 1) = 0

y' = f (-1, 0) = 1

y' = f (2, -2) = 0

From here, you can get particular solutions that pass through a certain point by interpolating the slopes of the tangents to the solution. I've attached a slope field for the example here at the points listed above. (In the order red, green, black). Each light gray arrow in the background shows the slope of the tangent line.

If you're still unsure how the slope field is generated, I suggest looking up videos on the subject. The process is a bit difficult to describe without a dynamic visual aid.