Expert: Sherman D. - 3/21/2004

Question
Its a new quarter and its already time for another test! Its crazy I know, but anyway heres the problems we have been told we must know how to do:

1.Initually theres 1000 bacteria in a culture, the number of bacteria doubles each hour, number of bacteria after t hours can be found using the formula N=1000(2t) how many bacteria after 10 hours?

2.there are 4500 bacteria, they double each hour, number after t hours can be found using formula N=4500(2t) how long will it take to grow 55,000 bacteria?

3.graph f(x)=2(1/2)^n

4.simplify 6e^19
          _____
          8e^6

5.if $1000 is invested at a rate of 5% after 2 years compound continuorsin find the balance in the equation using A=Pe^rt

6.evaluate log525 (five by log is smaller then 25)

7.graph y=log4X (x is larger then 4)

8.express as a single logarythem
loga8+loga35

9.expand using the properties of logarythem
 3xy^3
 _____
 Z^4

10. R=log10, R is measurement of ricter scale I is intensity, find ricter scale measurement of an earthquake intensity 103,000,000

11. solve for x, round to nearest hundreath
   1^56=33

12. evaluate to three decimal places e1.35

13. evaluate the expression log1115 125

14. evaluate log12782 to three decimals (the 12 by log is smaller)

15. expand the expression log^3(x^-2y^3)

16. express as a single logarythem logc12+logc55

17.solve for x correct to four decimal places e7x=8.4

18. solve 135log^6^x=18

19. solve 6^-^0^.^2^x-3=7

20. solve 27=9^7^x^+^3

again thanks so much for your time, you have truley been of a great help to me!  

Answer
Logarithmic and Exponential info found at http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/calctopic1/logs.html

1.)
N = 1000(2(10))
N = 1000(20)
N = 20000

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2.there are 4500 bacteria, they double each hour, number after t hours can be found using formula N=4500(2t) how long will it take to grow 55,000 bacteria?

55000 = 4500(2t)
(550/45) = 2t
(110/9) = 2t
Divide both sides by 2
t = 110/18
t = 55/9
t = 6.11111111111 hours
or
t = 6 hours, 6 minutes, 40 seconds

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3.) graph
f(x) = 2(1/2)^n
for a graph, go to www.calculator.com, click graphing, then type in 2((1/2)^x), making sure to leave out the y = or f(x) = part, or the graph will not work or show up. Also i had to use "x" instead of "n" since the site doesn't understand anything but "x", or you can go to www.quickmath.com

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4.
simplify
(6e^19)/(8e^6)

(6/8) * e^(19 - 6)
(3/4) * e^13
Answer : (3e^13)/4

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5.)if $1000 is invested at a rate of 5% after 2 years compound continuosly, find the balance in the equation using
A = Pe^rt
e = 2.71828
P = 1000
r = 5/100
t = 2

A = 1000 * (2.71828)^((5/100) * 2)
A = 1000 * (2.71828)^((1/20) * 2)
A = 1000 * (2.71828)^(2/20)
A = 1000 * (2.71828)^(1/10)
A = 1000 * (1.10517084373603)
A = $1105.17

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The only way that i know how to solve for logarithmic problems, is by converting them to exponential problems. Same for graphing.

6.
evaluate
log(base(5))25 = (log 25)/(log 5)

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7.)graph
y = log(base(4))x

y = (log x)/(log 4)

Go to www.calculator.com, click graphing, and type in
(log(x))/(log(4)) to get your graph.

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The "a" in () just means base "a"
8.)
express as a single logarythem
loga8 + loga35

log(a)8 + log(a)35
log(a)(8 * 35)
log(a)280

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9.) sorry, i don't think i can help you on this one. Its been awhile since i did problems like these. I can do problems if i can find a website that will show me how to do it.

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10.) R = log10, R is measurement of ricter scale I is intensity, find ricter scale measurement of an earthquake intensity 103,000,000.
Sorry, but i don't see an "I" in this problem. So you will have to send this one back to me.

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11.) If by this you mean
solve for x, round to nearest hundreath

x^56=33
56thrt both sides and you get
x = 56thrt(33)
x = 1.06

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12.) If by this you mean
evaluate to three decimal places e^1.35
(2.71828)^1.35
3.857

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13.) If by this you mean
evaluate the expression
log(base 1115) 125
(log 125)/(log 1115)
.688126311

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14.)
evaluate log(base 12)782
(log 782)/(log 12)
2.681

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15.) If by this you mean
expand the expression log(base 3 )(x^-2y^3)
log(base 3)x^-2 + log(base 3)y^3

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16. express as a single logarythem logc12+logc55
logc(12 * 55)
logc(660)

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17.) If by this you mean
solve for x correct to four decimal places e^(7x) = 8.4
y = ln(x)
e^y = x

FOund at http://web.mit.edu/wwmath/calculus/differentiation/ln.html3

7x = ln(8.4)
x = (ln(8.4))/7
x = .3040

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18.) Sorry, can't really help you on this one.

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19.) solve 6^-^0^.^2^x-3=7, You will have to tell me what you meant.

20.) solve 27=9^7^x^+^3, You will have to tell me what you meant.