Question

Use 2 methods to predict the output for an input of 200.

Answer 1

Given a table represents a relation between x and y

As shown, the change of (x) and (y) vary with a constant rate

So, the table represents a linear function

The general equation will be: y = m * x + b

where (m) is the slope, (b) is the value of y when (x=0)

So, from the table, when x = 0 , y = 25

The slope will be as follows:

`m=(30-25)/(1-0)=(5)/(1)=5`

So, the equation will be:

`y=5x+25`

When the input = 200, x = 200

So, substitute with (x) to find the output (y)

`y=5\cdot200+25=1000+25=1025`

So, the answer will be:

For an input 200, the output is 1025

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Another method to solve using the arithmetic sequence.

As shown in the table consider (x) represents the number of terms

So, (y) will be an arithmetic sequence

The first term = a = 30

The common difference = d = 35 - 30 = 5

the general rule of the arithmetic sequence is:

`y_{}=a+d(x-1)`

substitute with (a) and (d)

`y=30+5(x-1)`

When x = 200

`y=30+5(200-1)=30+5\cdot199=1025`

So, for an input 200, the output = 1025