Question

Joe is going to travel to Dallas. He lives 360 miles away and can average 60 miles per hour. Write a linear model that represents Joe's distance from Dallas, d(t), traveled as a function of time, t, in hours.
a.
d(t) = 360 - 60t
c.
d(t) = 360t + 60
b.
d(t) = 60t
d.
d(t) = 360 + 60t

Answer 1

Sales at a certain department store follow the model y=85-13.254x where y is the total sales in thousands of dollars and x is the number of years after 2001. What was the first year that sales fell below $50,000?
a.
1999
c.
2004
b.
1998
d.
2005

Answer 2

In your 1st problem... once Joe leaves his home toward Dallas... the distance he traveled governed by the formula\[\large{d_{home}(t)=60t}\]but that is the distance Joe traveled from home not to Dallas, and since Dallas is 360 miles from his home, if we will going to deduct his distance traveled, we're able to determine his distance from Dallas such that\[\large{d_{Dallas}(t)=360-60t}\]

Answer 3

In your 2nd problem... we can solved first the number of years where the sales is exactly $50,000; since \(y\) is the total sales in thousand dollars, we can set \(y=50\)... therefore \[50=85-13.254x\]\[50-85=-13.254x\]\[-35=-13.254x\]\[x=\frac{-35}{-13.254}\]\[x\approx2.64~years\]that will be at the end of 3rd year from 2001, so the year that we are looking for is\[\large{Year=2001+3=2004}\]You can check it by plugging 3 in place of x, to prove that y < 50 (or $50,000).