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Is the Port Townsend sales price ever
double the Seattle sales price?

Is The Port Townsend Sales Price Ever Double The Seattle Sales Price class=

Sagot :

Using linear functions, it is found that the sales price in Port Townsend is never double the Seattle price.

A linear function has the following format:

[tex]y = mx + b[/tex]

In which:

  • m is the slope, which is the rate of change.
  • b is the y-intercept, which is the initial value.

For Seattle:

  • Initial value of $38,000 in 1970, thus the y-intercept is [tex]b = 38000[/tex].
  • Increased by $137,000 in 20 years, thus the slope is:

[tex]m = \frac{137000}{20} = 6850[/tex]

Thus, the sales prince in n years after 1970 for Seattle is:

[tex]S(n) = 38000 + 6850n[/tex]

For Port Townsend:

  • Initial value of $8,400 in 1970, thus the y-intercept is [tex]b = 8400[/tex].
  • Increased by $160,000 in 20 years, thus the slope is:

[tex]m = \frac{160000}{20} = 8000[/tex]

Thus, the sales prince in n years after 1970 for Port Townsend is:

[tex]P(n) = 8400 + 8000n[/tex]

Port Townsend is double Seattle in n years after 1970, for which:

[tex]P(n) = 2S(n)[/tex]

Then

[tex]8400 + 8000n = 2(38000 + 6850n)[/tex]

[tex]8400 + 8000n = 76000 + 13700n[/tex]

[tex]7500n = -67600[/tex]

Negative number, and we are working only with positive, thus, it is found that the sales price in Port Townsend is never double the Seattle price.

A similar problem is given at https://brainly.com/question/23861861

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