# Thread: 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 $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double. I have the following: A = Pe^rt A = 600e^(5.64)(t) 1200 = 600e^(5.64)(t) 2 = e^(5.64)(t) ln(2) = ln(e)^(5.64)(t) ln(2) = 5.64t (ln(2))/5.64 = t Is this correct? 7. A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another 5 minutes, etc. How long until 100 million computers are infected? 2. 1) I assume that you mean$\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}$Just plug that into your calculator and you have your answer. 2) Yes that is correct. 3) Let's call the number of computers infected$\displaystyle I$. We know that after 5 minutes, 20 computers are infected, plus the original 1. We also know that exponentials are of the form:$\displaystyle y = ke^ {rt}$So we then have:$\displaystyle I(t) = 21e^ {4t}$To find how long until 100,000,000 computers are infected, simply set the equation equal to 0 and solve for$\displaystyle t\$ using the method from question 1.