Posted: November 13th, 2015

Pre-Calculus

In 1975, I bought an old Martin ukulele for $300. In 1995, a similar uke was

selling for $1200. In 1980,

I bought a new Kamaka uke for $75. In 1990, I sold it for $325.

(a) Give a linear model relating the price p of the Martin uke to the year t. Take

in 1975.

p(t) =

(b) Give a linear model relating the price q of the Kamaka uke to the year t. Again

take in

1975.

q(t) =

(c) In what year is the value of the Martin twice the value of the Kamaka?

(d) Give a function f(t) which gives the ratio of the price of the Martin to the

price of the

Kamaka.

f(t) =

(e) In the long run, what will be the ratio of the prices of the Martin ukulele to

the Kamaka

ukulele?

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t = 0

t = 0

2. –/12 pointsUWAPreCalc1 14.P.004.

Isobel is producing and selling cassette tapes of her rock band. When she had sold

10 tapes, her net

profit was $4. When she had sold 20 tapes, however, her net profit had shrunk to $2

due to increased

production expenses. But when she had sold 30 tapes, her net profit had rebounded

to $10.

(a) Give a quadratic model relating Isobel’s net profit y to the number of tapes

sold x.

y =

(b) Divide the profit function in part (a) by the number of tapes sold x to get a

model relating

average profit w per tape to the number of tapes sold.

w =

(c) How many tapes must she sell in order to make $2.03 per tape in net profit?

(Enter your

answers as a comma-separated list. Round your answers to the nearest whole number.)

tapes

Additional Materials

Reading

3. –/12 pointsUWAPreCalc1 14.P.005.

Find the linear-to-linear function whose graph passes through the points and

f(x) =

What is its horizontal asymptote?

y =

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4. –/12 pointsUWAPreCalc1 14.P.006.

Find the linear-to-linear function whose graph has as a horizontal asymptote and

passes through

f(x) =

Additional Materials

Reading

5. –/12 pointsUWAPreCalc1 14.P.008.

A street light is 9 feet above a straight bike path. Olav is bicycling down the

path at a rate of 15 MPH. At

midnight, Olav is 33 feet from the point on the bike path directly below the street

light. (See the

picture.) The relationship between the intensity C of light (in candlepower) and

the distance d (in feet)

from the light source is given by where k is a constant depending on the light

source.

(1, 1), (4, 2) (30, 3).

y = 6

(0, 10) and (2, 8).

C = , k

d2

(a) From 21 feet away, the street light has an intensity of 1 candle. What is k?

k =

(b) Find a function which gives the intensity I of the light shining on Olav as a

function of time t,

in seconds.

I(t) =

(c) When will the light on Olav have maximum intensity? (Round your answer to one

decimal

place.)

t = s

(d) When will the intensity of the light be 2 candles? (Enter your answers as a

comma-separated

list. Round your answers to two decimal places.)

t =

s

Additional Materials

Reading

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