The price of a widget was $299. In five years, the price dropped to $149. Assume a linearly trend. (a) Find a linear model P = ax + b, where P is the price at any time x. (b) Use this model to predict the price in 7 years. 12.

If the price of a widget was $299, and the price dropped to $149 in 5 years, then:

a) The linear model is P  =  -30x  +  299

b) The price in 7 years is $89

The original price of the widget, b = $299

The price after 5 years, P = $149

The number of years, x = 5

The given model is P = ax  +  b

Substitute x = 5, P = 149, and b = 299 into the equation to solve for a.

149  =  5a   +  299

5a  =  149  -  299

5a  =  -150

a   =  -150/5

a  = -30

To get the linear model, substitute a = -30 and b = 299 into the equation

P = ax + b

P  =  -30x  +  299

a) The linear model is P  =  -30x  +  299

To get the price in 7 years, substitute x = 7 into the linear model in part a.

P  =  -30x  +  299

P  =  -30(7)  +  299

P  =  -210  +  299

P  =  89

The price in 7 years is $89

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The calculation is as follows:

Step-by-step explanation:

The computation is shown below:

a. According to the question, the data is given

P = ax + b

When x = 0 the P is $299 = b = 299

And, when x = 5 the P is $149 i.e.

5a + $299  = $149

5a = -$150

a = -$30

Here the equation would be

P = -$30x + $299

b. If x = 7

So,

P = -30(7) + $299

= -$210  + $299

= $89

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