A few calculus questions
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A few calculus questions

[From: ] [author: ] [Date: 12-08-09] [Hit: ]
will triple the size of your account in 5 years,1.0986...1.......
1) what interest rate, compounded continuously, will triple the size of your account in 5 years, to the nearest percent
2)express log(7)13 in terms of natural logarithms
3)express 13^n as a power of e
4)differentiate:
Y=log(2x)
Y=x2^x

Any help is appretiated

-
1) 3A = A e^(x)
3 = e^x
ln 3 = x
1.0986... = x

1.10%

2) log_7 13 = ln 13/ln 7

3) 13^n = e^x
n ln 13 = x

4) y = log (2x)
dy/dx = 1/(2x) • 2/ ln 10 = 2/(2x ln 10) = 1/(x ln 10)

y = x 2^x
dy/dx = 2^x ln 2 + x 2^x
1
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