# Exponential Functions/Logs Questions -- Help!

• Feb 12th 2008, 12:09 PM
MathGeek06
Exponential Functions/Logs Questions -- Help!
2 .Assume that the number of viruses present in a sample is modeled by
the exponential function f(t) = 10t, where t is the elapsed time in
minutes.

How would you apply logarithms to determine when the sample will grow
to 5 billion viruses?

4. Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double. I have the following: A = Pe^rt A = 600e^(5.64)(t) 1200 = 600e^(5.64)(t) 2 = e^(5.64)(t) ln(2) = ln(e)^(5.64)(t) ln(2) = 5.64t (ln(2))/5.64 = t Is this correct? 7. A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another 5 minutes, etc. How long until 100 million computers are infected? • Feb 12th 2008, 01:24 PM a tutor Quote: Originally Posted by MathGeek06 2 .Assume that the number of viruses present in a sample is modeled by the exponential function f(t) = 10t, where t is the elapsed time in minutes. How would you apply logarithms to determine when the sample will grow to 5 billion viruses? I assume you mean$\displaystyle f(t)=10^t$Solve$\displaystyle 10^t=5 billion$Remember$\displaystyle log(10^t)=tlog(10)$Using base 10 you get$\displaystyle t=log(5 billion)$Quote: Originally Posted by MathGeek06 4. Maya has deposited$600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double.

Try $\displaystyle 1200=600$x$\displaystyle 1.0564^t$

Quote:

Originally Posted by MathGeek06
7. A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another 5 minutes, etc. How long until 100 million computers are infected?

1+20+400..... This is a geometric series.
• Feb 12th 2008, 06:00 PM
MathGeek06
Thanks a tutor!

Is it possible that someone can be more specific in helping me answer the last question about the computer virus. I see that it is a geometric series, but I am still not sure how to go about getting the answer to the question.
• Feb 13th 2008, 02:11 AM
a tutor
first term a=1
common ratio r=20

Sum of first n terms $\displaystyle S_n=\frac{a(1-r^n)}{1-r}$

In this case $\displaystyle 10^8=\frac{1-20^n}{1-20}$