Correction

Test 5 College Algebra Chapter 6 Show all required work.. 1) Given: 2( ) 3 4 7 ( ) 2 1f x x x and g x x= − − = − 9 pts a) Find f(g(x)) b) Find f(g(-1))

2) Given: 3 4( ) ( ) 4 2

f x and g x x x

= = − +

, 10 points

a) State the domain for f(x) and g(x). b) Find f(g(x)), show all work. c) State the domain for f(g(x)).

3) Given: 3 2( ) 4

xf x x +

= −

10 points

a) State the domain and range of f(x) b) Find f-1(x), show all work c) State the domain and range of f-1(x)

For #s 4 – 11, Solve the following problems, show all work. Exact answers only, no decimal answers. 7 points each 4) 4log (x+2) = 3 5) ln (x + 1) = 3 6) ln(x - 5) + ln(x+2) = ln (8) 7) ln(x +5) - ln(x-2) = ln (4)

8) 3 15x = 9) 42x = 21 10) 1 12 5x x+ −= 11) ex+2 = 3x – 1

Solve the following using the compound interest formulas. 5 pts each

Future Value: (1 )ntrA P n

= + , rtA Pe=

Present Value: (1 ) ntrP A n

−= + , rtP Ae−=

12) If you invest $7500 at 13 4

% interest compounded quarterly, how much will you have in 12

yrs? 13) If you invest $10,000 at 2.75% interest compounded continuously, how much will you have in 8 yrs? 14) If you need $100,000 in 18 years, how much should you invest now if you can get 2.5% compounded continuously?

15) The amount of bacteria present in a culture at time t in hours obeys the function N(t) = 900e.13t 15 points a) Determine the number of bacteria at t = 0 hours? b) What is the growth rate of the bacteria? c) What is the population after 4 hours? d) When will the population reach 2500? e) How long will it take to double?

Problems 16 & 17 are 10 points each. 16) If a population grows from 60,000 to 90,000 in 6 years, how long will it take to double? a) Find k, round to 4 decimals, show all work b) Find solution, round to 2 decimals, show all work 17) The half life of uranium is 69 years. How long will it take uranium to reach 25% of its original value? a) Find k, round to 2 decimals, show all work b) Find solution, round to 2 decimals, show all work

18) The World Wildlife Fund has placed a certain amount of rare elephants in a conservation

area in Borneo. The number of elephants is given by P(t) = .14

1900 1 .9 te−+

, where t is the time in

years. 15 points a) What is the carrying capacity? b) What is the growth rate? c) What is the initial population? d) How long will take to reach 1250 elephants?