Question

the number of words in some code increased approximately lineraly from 1.7 million words in 1955 to 7.9 million words in 2005. Predict the number of words in the code in 2035

Answer 1

Answer:

The number of words in the code in 2035 will be 11.62 million words

Step-by-step explanation:

Let

x -----the number of years since 1955

y ----> the number of words in some code in millions

$2005-1955=50\ years$

we have the points

(0,1.7) and (50,7.9)

Find the slope m

$m=(7.9-1.7)/(50-0)\\m=6.2/50\\m=0.124$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=0.124\\b=1.7$

substitute

$y=0.124x+1.7$

Predict the number of words in the code in 2035

$x=2035-1955=80\ years$

substitute in the equation

$y=0.124(80)+1.7$

$y=11.62$

therefore

The number of words in the code in 2035 will be 11.62 million words

Answer 2

11.62 million words

Further explanation

Given:

The number of words in some code increased approximately linearly from 1.7 million words in 1955 to 7.9 million words in 2005.

Question:

Predict the number of words in the code in 2035.

The Process:

• A line that is not parallel to either the x-axis or the y-axis represents a line that occupies a slope or in other words a gradient.
• The gradient or steepness of a straight line is the rate at which the line rises or falls. The gradient is the same at any point along a straight line.
• The symbol m is used to represent the gradient or slope.

In general, the gradient of the line joining the points A(x₁, y₁) and B(x₂, y₂) is given by the formula:

$\boxed{\boxed{ \ m = \frac{y_2 - y_1}{x_2 - x_1} \ }}$

In the Cartesian coordinate system, the x-axis represents years while the y-axis represents the number of words in some code.

• x₁ = 1955
• x₂ = 2005
• y₁ = 1.7 millions words
• y₂ = 7.9 millions words

So, there are two points namely (1955, 1.7) and (2005, 7.9).

Let us find out the gradient.

$\boxed{ \ m = \frac{7.9 - 1.7}{2005 - 1955} \ }$

$\boxed{ \ m = \frac{6.2}{50} \ }$

$\boxed{ \ m = \frac{12.4}{100} \ } \rightarrow \boxed{\boxed{ \ m = 0.124 \ }}$

And now, we will predict the number of words in the code in 2035. We can use the point (1955, 1.7) as (x₁, y₁) together with the point (2035, y).  

• x₁ = 1955
• x₂ = 2035
• y₁ = 1.7 millions words
• y₂ = y millions words

Recall that the value of the gradient remains 0.124.

$\boxed{ \ 0.124 = \frac{y - 1.7}{2035 - 1955} \ }$

$\boxed{ \ y - 1.7 = 80 \times 0.124 \ }$

$\boxed{ \ y - 1.7 = 9.92 \ }$

$\boxed{\boxed{ \ y = 11.62 \ }}$

Thus, the number of words in the code in 2035 is 11.62 million words.

- - - - - - -

Notes

We can form the line function first.

$\boxed{ \ Point-slope \ form: y - y_1 = m(x - x_1) \ }$

$\boxed{ \ m = 0.124 \rightarrow y - y_1 = 0.1242(x - x_1) \ }$

The line passing through the point (1955, 1.7), we choose one.

$\boxed{ \ x_1 = 1955, y_1 = 1.7 \ } \rightarrow \boxed{ \ y - 1.7 = 0.124(x - 1955) \ }$

For x = 2035, $\boxed{ \ y - 1.7 = 0.124(2035 - 1955) \ }$

$\boxed{ \ y - 1.7 = 0.124(80) \ }$

$\boxed{ \ y - 1.7 = 9.92 \ }$

$\boxed{\boxed{ \ y = 11.62 \ }}$

Learn more

1. Finding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992
2. Determine the equation represents Nolan’s line  brainly.com/question/2657284  
3. Find the missing endpoint if the midpoint is known brainly.com/question/5223123

Keywords: the number of words, in some code, increased, approximately, linearly, from, 1.7 million words, 1955, 7.9, 2005, predict, 2035, slope, gradien, linear function