Question

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

Answer 1

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:

$y = mx + b$

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 $b = 38000$.

• Increased by $137,000 in 20 years, thus the slope is:

$m = \frac{137000}{20} = 6850$

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

$S(n) = 38000 + 6850n$

For Port Townsend:

• Initial value of $8,400 in 1970, thus the y-intercept is $b = 8400$.

• Increased by $160,000 in 20 years, thus the slope is:

$m = \frac{160000}{20} = 8000$

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

$P(n) = 8400 + 8000n$

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

$P(n) = 2S(n)$

Then

$8400 + 8000n = 2(38000 + 6850n)$

$8400 + 8000n = 76000 + 13700n$

$7500n = -67600$

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 brainly.com/question/23861861