3. In a computer network, a computer virus is spreading. The number of infected computers is determined by the formula $N(t)=30 \cdot e^{0.1 t}$, where $N$ is the number of infected computers and $t$ is the time in minutes.

a) What is the maximum number of computers infected in one hour?

b) How many minutes are needed at minimum for the virus to infect 60000 computers?
3. We calculate the number of infected computers in one hour $N(60)=30 \cdot e^{6} \doteq 12102.8$. In one hour, there are thus at most 12102 infected computers. We write the equation $60000=30 \cdot e^{0.1 t}$. Taking the logarithm, $0.1 t \ln e=\ln 2000$. We get the solution $t=\frac{\ln 2000}{0.1} \doteq 76.009$. For the virus to infect 60000 computers, it takes at least 77 minutes.

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=63&width=1630&top_left_y=2284&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=54&width=1627&top_left_y=2337&top_left_x=206)

Write the answer............................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=54&width=1627&top_left_y=2440&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=57&width=1627&top_left_y=2487&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=62&width=1627&top_left_y=2536&top_left_x=206)

Write the answer..............................................................................................