P2 AND P3 DOUBT PLZZZZZ HELP SOLVING....

[Sweet_angel]

Hey anyone plzzzzzz...... solve my doubt m nt able to solve this.....


1.) Jacques is saving for a new car which will cost $29000 . He saves by putting $400 a month into a savings account which gives 0.1% interest per month . After how many months will he be able to buy his car ? Assume it does not increase in price !
ANS : 71 (P2/P3 chap-3 ex.3C ques 8)

2.) A biological culture contains 500000 bateria at 12 noon on Monday. The culture increases by 10% every hour. At what time will the culture exceed 4 million bacteria ?
ANS : 9.45 a.m. Tuesday (P2/P3 chap-3 ex.3C ques 10)

3.) A dangerous radioactive substance has a half-life of 90 years . It will be deemed safe when its activity is down to 0.05 of its initial value . How long will it be before it is deemed safe ?
ANS : 389 years (P2/P3 chap-3 ex.3C ques 11)

4.) Solve the following equation to find x in terms of a where a>0 and a is not equal to 100
a.) 2log(2x)=1+log a
ANS : squareroot(5a/2) (P2/P3 chap-3 miscellaneous exercise 3 ques. 1(b))

5.) The function f is given by f : x I--> log (1 + x) , where x belongs to R and x > -1 . Express the definition of f^(-1) in a similar form.
ANS : f^(-1) : x I--> e^x (-1) , x belongs to R (P2/P3 chap-3 miscellaneous exercise 3 ques. 3)





PLZ PLZ PLZ..... HELP ME OUT SOLVING THESE SUMS.... PLZZZZ..... :?

 

[Sweet_angel]

hey guyzz......plzzzzzzzzzzzz.......solve my doubt plzzzzz.....plzzzz......plzzzzzzz....
ne1????? plzzzzzzzzz
wud b really thankful.....plzzz..... :?

 

[soumayya]

4)
2 log 2x = 1+ log a
log (2x)^2 = log 10 + log a
log 4x^2 = log 10a
4x^2 = 10a
x^2 = 5a/2
x = √5a/2

 

[soumayya]

5.) The function f is given by f : x I--> log (1 + x) , where x belongs to R and x > -1 . Express the definition of f^(-1) in a similar form.
ANS : f^(-1) : x I--> e^x (-1) , x belongs to R (P2/P3 chap-3 miscellaneous exercise 3 ques. 3)

shouldn't it b ln instead of log..??

 

[soumayya]

5)
f(x) = ln (1+x)
Let y = f(x)
y = ln (1+x)
e^y = 1+x
x = e^y -1
f^(-1)= e^x - 1

 

[soumayya]

3.) A dangerous radioactive substance has a half-life of 90 years . It will be deemed safe when its activity is down to 0.05 of its initial value . How long will it be before it is deemed safe ?
ANS : 389 years (P2/P3 chap-3 ex.3C ques 11)

constructing a geometric progression...taking the first term to B 1...

1, 0.5, 0.25,...
a= 1, r = 0.5
let ar^(n-1) = 0.05
0.5^(n-1)= 0.05
taking log on both sides...
(n-1) log 0.5 = log 0.05
n-1= 4.322

we don't count the 1st term since it did not take 90 yrs to become 1...so we use the value obtained for (n-1)
ans: 4.322 * 90 = 389 yrs...

Alternatively u could make 0.5 the 1st term..

 

[soumayya]

2.) A biological culture contains 500000 bateria at 12 noon on Monday. The culture increases by 10% every hour. At what time will the culture exceed 4 million bacteria ?
ANS : 9.45 a.m. Tuesday (P2/P3 chap-3 ex.3C ques 10)

constructing a geometrical progression..
500 000, 550 000, ....
a= 500 000, r = 1.1

ar^(n-1) > 4 000 000
500 000 * 1.1^(n-1) > 4 000 000
1.1^(n-1) > 8
taking log on both sides...
(n-1) log 1.1 > log 8
n-1 > 21.82

we don't count the first term since it did not take 1 hr for the culture to become 500 000...
ans: 12 00 + 21 hrs 49 min = 09 49 on tuesday