College Algebra 10 questions MASTER TUTOR 2011 Only

1. 4t The temperature T, in degrees Fahrenheit, of a person during an illness is given by the function T(0 =

- + 98.6, where

t'+1 t = time, in hours. Find the interval over which the temperature wa$ over 100o.

The interval is between and hours. (Enter the lower number first. Round to the nearest hundredth.)

2. I The magnitude R, measured on the Richter scale, of an earthquake of intensity I is defined as R = lo9 l0 where lo is a

minimum intensity used for comparison. lf the intensity of an earthquake was fil'75 .ls, what was the magnitude on the Richter scale?

The magnitude of the earthquake was . (Simplifu your answer.)

3. The demand for lumber is increasing exponentially. The amount of timber N, in billion cubic feet, consumed t years after 1997 can be approximated by N(t) = 71(1.01S)t, where t= 0 conesponds to 1997.

How much lumber was consumed in 1998?

billion cubic feet

(Round to the nearest hundredth.)

How much lumber was consumed in 2000.

billion cubic feet

(Rourd to the "earest

hundredth.)

How much lumberwas consumed in 2010.

billion cubic feet

(Round to the nearest hundredth.)

4. 4O+2x A baseball team determines that the cost per player of a group hitting lesson is given by the formula C(x) = -;-, where x is the number of players in the group and C(x) is in dollars. Complete parts a through c below.

a) Determine the cost per player of a group hitting lesson when there are 2, 5, and 8 players in the group.

The cost per player of a group hitting lesson when there are 2 players in the group is $ , there are 5 players in the group is $ , and there are 8 players in the group is $ (Simplify your answers. Type an integer or a decimal.)

b) Find a formula for the inverse of the function and explain what it represents. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

C A' eformulafortheinverseofthefunctionisC-t(r)=- . - C-1(")representsthenumberofplayers in the group lesson, where x is the cost per player, in dollars. O B' ntormulafortheinverseof thefunction isC-'(*)=_ - _,_ C-1(") representsthecostper

player, in dollar$, where x is the number of players in the group lesson.

c) Use the inverse function to determine the number of players in the group lesson when the cost per player is $42, $12, and $7.

There are

There are

There are

player(s) in the group lesson when the cost per player is $42.

player(s) in the group lesson when the cost per player is $12.

player(s) in the group lesson when the cost per player is $7.

5. The total amount of spending per year, in billions, on pets in a) The total amount of spending on pets in 2AA2 is about a certain country x years after 2000 is given by the following $ Uiilion. function.

P(x) = 2.17g'x+ 25.3

a) Determine the total amount of spending per year on pets $ in2AO2 and in 2013.

b) Find p- 1(*) and explain what it represenls.

(Round to one decimal place as needed.)

The total amount of spending on pets in 2013 is about billion.

(Round to one decimalplace as needed.)

b) Find P-1(*).

-4P '(x) = (Do not sim6tiry)- What does p - 1 (") represent? Choose the correct answer below.

C A' p - 11*1 ,"pr"""nts the number of yearc after 2000 thi year.

O B' p - 11x1 represents the total amount of spending per y after 2000.

6' The supply tunction and demand tunction for the sale of a certain type of DVD player are given by S(p) = 140e 0'00sP and D(p) = r148e

- 0'002p, where S(p) is tre number of DVD players that the company is willing to sell at price p and D(p) is the quantity that the public is willing to buy at price p. Find p such that D(p) = S(p). This is called the equilibrium price.

The equilibrium price is about $ (Do not round untilthe final ansil'eTie-n round to two decimal places as needed.)

7. I -.Theloudness, L, indecibels(dB), isgivenbytheformulaL=10.loS l0,wherels -10-12 Wlm2.Theintensity,l,of a

sound is 5.2 x 10 - 6 w / m2 . How loud in decibels is this sound level?

The loudness is approximately _ dB. (Round to the nearest whole number as needed.)

8. The number of concurrent users of a social networking site has increased dramatically since 2005. By 2014, this social networking site could connect concurrently 70 million users online. The function P(t)= 2.a59,r,475)t, where t is the number of years after 2005, models this increase in millions of users, Estimate the number of users of this site that could be online concunently in 2006, in 2010, and in 2013. Round to the nearest million users.

The number of users of this site that could be online concunently in 2006 is approximately (Round to the nearest whole number.)

The number of users of this site that could be online concunently in 2010 is approximately

(Round to the nearest whole number.)

The number of users of this site that could be online concurrently in 2013 is approximately

(Round to the nearest whole number.)

million.

million.

million.

L Find the nonlinear asymptote of the following function.

x5 *4x3 *Gx2 r1a1 - --J-

x'+4

The nonlinear asymptote is y=

10. Following the birth of a child, a parent wants to make an initial investment Pg that will grow to $60,000 for the child's education at age 18. lnterest is compounded continuously at 6%. what should the initial investment be? such an amount is called the present value of $60,000 due 18 years from now'

The present value is about $_" (Do not round until the final answer. Then round to two decimal places as needed.)