hiy\a
Badges: 10
Rep:
?
#1
Report Thread starter 2 weeks ago
#1
A sum of money is invested in a savings account withba compound interest rate of r% paid annually. T is the number of years taken for the investment to be worth twice the sum invested.a) Express in the form loga(b) where b is an integer.b) Money invested in a simple interest account with an annual interest rate of p% takes twice as long to double in value as money in a compound interest account with annual interest rate q%End of QSo far for part a ive gotten T=log2/log(100 r/100) but idk how to simplify furtherBut for part b i have no idea where to start
0
reply
mqb2766
Badges: 18
Rep:
?
#2
Report 2 weeks ago
#2
(Original post by hiya)
A sum of money is invested in a savings account withba compound interest rate of r% paid annually. T is the number of years taken for the investment to be worth twice the sum invested.a) Express in the form loga(b) where b is an integer.b) Money invested in a simple interest account with an annual interest rate of p% takes twice as long to double in value as money in a compound interest account with annual interest rate q%End of QSo far for part a ive gotten T=log2/log(100 r/100) but idk how to simplify furtherBut for part b i have no idea where to start
Can you change the base in a). If b is an integer it suggests base a is a function of r? Are you sure a) is T = , can you upload a pic of the question?
Last edited by mqb2766; 2 weeks ago
0
reply
hiy\a
Badges: 10
Rep:
?
#3
Report Thread starter 2 weeks ago
#3
(Original post by mqb2766)
Can you change the base in a). If b is an integer it suggests base a is a function of r? Are you sure a) is T = , can you upload a pic of the question?
Name:  8F955EBC-AABD-4568-AB0D-7A3A019483B0.jpeg
Views: 10
Size:  55.4 KB
0
reply
hiy\a
Badges: 10
Rep:
?
#4
Report Thread starter 2 weeks ago
#4
(Original post by hiya)
Name:  8F955EBC-AABD-4568-AB0D-7A3A019483B0.jpeg
Views: 10
Size:  55.4 KB
Here is the mark sheme also
Name:  43877313-5402-40FC-BC3C-D68AB7F61DAD.jpeg
Views: 8
Size:  161.1 KB
0
reply
mqb2766
Badges: 18
Rep:
?
#5
Report 2 weeks ago
#5
(Original post by hiya)
Here is the mark sheme also
Name:  43877313-5402-40FC-BC3C-D68AB7F61DAD.jpeg
Views: 8
Size:  161.1 KB
So what is confusing? If you have
y = a^x
Then
log_a(y) = x
That's all they've done? x is T, y is 2 and the base a is (100+r)/100. If you'd taken logs with a different base, use the base change formula.
It is an unusual question, in that the base is a function of a variable.
Last edited by mqb2766; 2 weeks ago
0
reply
hiy\a
Badges: 10
Rep:
?
#6
Report Thread starter 2 weeks ago
#6
(Original post by mqb2766)
So what is confusing? If you have
y = a^x
Then
log_a(y) = x
That's all they've done? x is T, y is 2 and the base a is (100+r)/100. If you'd taken logs with a different base, use the base change formula.
It is an unusual question, in that the base is a function of a variable.
I understand the process of getting T=log base(100+r)/100 (2) in the required form but I was confused at how the mark scheme simplified T=log2/log(100+r)/100 into the required form..
0
reply
mqb2766
Badges: 18
Rep:
?
#7
Report 2 weeks ago
#7
(Original post by hiya)
I understand the process of getting T=log base(100+r)/100 (2) in the required form but I was confused at how the mark scheme simplified T=log2/log(100+r)/100 into the required form..
As in the previous reply, either use the log definition directly or use the change of base formula:
http://home.windstream.net/okrebs/page57.html
Last edited by mqb2766; 2 weeks ago
0
reply
hiy\a
Badges: 10
Rep:
?
#8
Report Thread starter 2 weeks ago
#8
(Original post by mqb2766)
As in the previous reply, either use the log definition directly or use the change of base formula:
http://home.windstream.net/okrebs/page57.html
I understand now! Thank you
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

What do you want most from university virtual open days and online events?

I want to be able to watch in my own time rather than turn up live (179)
28.59%
I want to hear more about the specifics of the course (104)
16.61%
I want to be able to dip in and dip out of lots of different sessions (58)
9.27%
I want to meet current students (52)
8.31%
I want to meet academics and the people that will be teaching me (50)
7.99%
I want to have a taster lecture or workshop to see what the teaching is like (126)
20.13%
My parents/guardians are more interested than me to be honest (37)
5.91%
Other things – I'll tell you in the thread (20)
3.19%

Watched Threads

View All