# Exponential Functions & Logarithms Questions

• Feb 12th 2008, 08:51 AM
MathGeek06
Exponential Functions & Logarithms Questions
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, 02:19 PM
topher0805
1) I assume that you mean \$\displaystyle f(t) = 10^t\$

When the sample is grown to 5,000,000,000 we have that:

\$\displaystyle 5000000000 = 10^t\$

Take the log of both sides:

\$\displaystyle
\log {5000000000} = t\log {10}\$

We know that \$\displaystyle \log {10} = 1\$, so:

\$\displaystyle
t = \log {5000000000}\$