1 A new computer monitor costs 220 The computer monitors val

(1) A new computer monitor costs $220. The computer monitor\'s value depreciates linearly to $72 in 4 years time. Write a formula which expresses its value, V, in terms of its age, t, in years. Use lower case t in your answer.

V(t) =

(2). In the year 2000, the population of Smithville was only 70 thousand people while Jonesville had a population of 646 thousand. If Smithville increases at the constant rate of 10 thousand people per year and Jonesville at the rate of only 2 thousand people per year, determine the following.
(a) In what year will the populations be equal?
(For example, if they will be equal in 14 years, report the year 2014)
This question accepts numbers in decimal form or scientific notation.

(b)   How many inhabitants will each town have when they are equal?
(For example, if there will be 999,000 people, type a 999 in the answer box.)
(3)The following table gives the annual sales (in millions) of compact discs and vinyl long playing records.

Year 1995 1996 1997 1998 1999 2000
DVD sales (in millions) 0 2 23 73 142   213
CD sales (in millions) 108   70 40   13 3 1
(a)   What was the average rate of change of annual sales of each of them between 1999 and 2000?

The average rate of change of sales of DVDs was ?

Preview Change entry mode million discs/year.
The average rate of change of sales of CDs was ?

Preview Change entry mode million records/year.
(b)   Interpret these results in terms of sales.
DVD sales are a(n) function of CD sales....Decrease or increase?

(4)Some porcupines and hedgehogs are introduced to a wilderness area.
Find possible formulas for the following linear population functions P and H.
(a) The population P of porcupines is 221 in month t = 0 and grows by 56 porcupines per month.

P(t) =

(b)The population H of hedgehogs is 60 in month t = 2 and 100 by month t = 6.

H(t) =
(5).
You need to rent a car and compare the charges of three different companies.
Company A charges 15 cents per mile plus 40 dollars per day.
Company B charges 5 cents per mile plus 48 dollars per day.
Company C charges 64 dollars per day with no mileage charge.
(a) Find formulas for the cost of driving cars rented from companies A, B, and C, in terms of x, the distance driven in miles in one day.
(b) Graph the costs for each company for 0 x 500. Put all three graphs on the same set of axes. Use this graph to find under what circumstances company A is the cheapest. What about Company B? Company C?
(a)  
Find formulas for the cost, in dollars, of driving cars rented from companies A, B, and C, in terms of x, the distance driven in miles in one day:
Company A: yA =
Company B: yB =
Company C: yC =

(b)   Assume you drive at most 500 miles. Complete the blanks.
Company A is cheapest if you drive between ?
Company B is cheapest if you drive between ?
Company C is cheapest if you drive between ?

(6). Let y = q(x) be defined by the graph in Figure:
(a)   Evaluate q(a)
(b)Solve the following equation for x:
q(x) = h
x =?

Solution

1) initial cost of computer = $ 220

after 4 years cost = $ 72

taking initial time t = 0

we have two points ( 0 , 220) and ( 4 , 72 )

slope = 72 - 220 / 4 - 0 = -148 /4 = -37

y = mt+ b

plugging the values of m and x , y

we get

220 = -37(0) + b

b = 220

hence, equation of cost is

V(t) = -37 t + 220

2) smithville population = 70,000

jonesville = 646,000

smithville increases at 10,000 per year

and Jonesville at the rate of only 2 thousand people per year

finding equation for each town

smithville population y1 = 10,000 x + 70,000

x is years after 2000

jonesville population y2 = 2000x + 646000

time when population is equal

setting both equations equal to each other and solving for x

10,000 x + 70,000 = 2000x + 646000

8000 x = 576000

x = 72

therefore, after 72 years from 2000 that is in 2072 population of both towns would be equal

b) at that time population of smithville will be

10,000 (72) + 70,000 = 790,000

and jonesville will be

2000(72) + 646000 = 790,000

so answer is 790 inhabitants