11.62 million words
<h3>
Further explanation</h3>
<u>Given:</u>
The number of words in some code increased approximately linearly from 1.7 million words in 1955 to 7.9 million words in 2005.
<u>Question:</u>
Predict the number of words in the code in 2035.
<u>The Process:</u>
- 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} \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%20m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%5C%20%7D%7D)
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} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20m%20%3D%20%5Cfrac%7B7.9%20-%201.7%7D%7B2005%20-%201955%7D%20%5C%20%7D)
![\boxed{ \ m = \frac{6.2}{50} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20m%20%3D%20%5Cfrac%7B6.2%7D%7B50%7D%20%5C%20%7D)
![\boxed{ \ m = \frac{12.4}{100} \ } \rightarrow \boxed{\boxed{ \ m = 0.124 \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20m%20%3D%20%5Cfrac%7B12.4%7D%7B100%7D%20%5C%20%7D%20%5Crightarrow%20%5Cboxed%7B%5Cboxed%7B%20%5C%20m%20%3D%200.124%20%5C%20%7D%7D)
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} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%200.124%20%3D%20%5Cfrac%7By%20-%201.7%7D%7B2035%20-%201955%7D%20%5C%20%7D)
![\boxed{ \ y - 1.7 = 80 \times 0.124 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20y%20-%201.7%20%3D%2080%20%5Ctimes%200.124%20%5C%20%7D)
![\boxed{ \ y - 1.7 = 9.92 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20y%20-%201.7%20%3D%209.92%20%5C%20%7D)
![\boxed{\boxed{ \ y = 11.62 \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%20y%20%3D%2011.62%20%5C%20%7D%7D)
Thus, the number of words in the code in 2035 is 11.62 million words.
- - - - - - -
<u>Notes</u>
We can form the line function first.
The line passing through the point (1955, 1.7), we choose one.
For x = 2035, ![\boxed{ \ y - 1.7 = 0.124(2035 - 1955) \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20y%20-%201.7%20%3D%200.124%282035%20-%201955%29%20%5C%20%7D)
![\boxed{ \ y - 1.7 = 0.124(80) \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20y%20-%201.7%20%3D%200.124%2880%29%20%5C%20%7D)
![\boxed{ \ y - 1.7 = 9.92 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20y%20-%201.7%20%3D%209.92%20%5C%20%7D)
![\boxed{\boxed{ \ y = 11.62 \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%20y%20%3D%2011.62%20%5C%20%7D%7D)
<h3>Learn more</h3>
- 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
- Determine the equation represents Nolan’s line brainly.com/question/2657284
- 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