# Math Help - Exponential Functions & Logarithms Questions

1. ## 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?

2. 1) I assume that you mean $f(t) = 10^t$

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

$5000000000 = 10^t$

Take the log of both sides:

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

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

$
t = \log {5000000000}$

2) Yes that is correct.

3) Let's call the number of computers infected $I$. We know that after 5 minutes, 20 computers are infected, plus the original 1. We also know that exponentials are of the form:

$y = ke^ {rt}$

So we then have:

$I(t) = 21e^ {4t}$

To find how long until 100,000,000 computers are infected, simply set the equation equal to 0 and solve for $t$ using the method from question 1.