Question

A biologist is observing the exponential growth pattern of a virus. She starts with 60 of the virus that grows at a rate of 20% per hour. She will check on the virus in 24 hours. How many viruses will she find? (Simplify your answer completely. Round your answer to the nearest whole number.)

Answer 1

Using the exponential growth formula with a growth rate of 20%, the number of viruses starting from 60 can be calculated after 24 hours. The calculation involves using the formula N = N0 * e^(rt), which calculates the future amount based on initial quantity, rate, and time.

Step-by-step explanation:

Exponential Growth of a Virus

The student is asking how many viruses will be present after 24 hours if the initial number is 60 and the growth rate is 20% per hour. To determine the number of viruses after 24 hours of exponential growth, we use the formula for exponential growth: N = N0 * e^(rt), where N0 is the initial amount, r is the growth rate, and t is the time in hours.

Here, the initial amount of virus N0 = 60, the growth rate r = 0.20 (20%), and the time t = 24 hours. The calculation is as follows:

Calculate the value of e^(0.20*24) using a scientific calculator.

Finally, round the result to the nearest whole number as the question requests.

Keep in mind that in the context of this question, the growth of viruses exhibits exponential behavior similar to bacteria, which reproduces at a constant rate in an environment with sufficient resources.

Answer 2

Since they grow exponentially, the number of viruses after t hours is given by the function:

`f(t)=f(0)\cdot(1+r)^t`

where f(0) is the initial number of viruses and r is the rate of growth.

In this problem, we have:

`\begin{gathered} f\mleft(0\mright)=60 \\ \\ r=20\%=(20)/(100)=0.2 \end{gathered}`

And after 24 hours, t = 24. So, the number of viruses she will find is f(24):

`f(24)=60\cdot(1+0.2)^(24)=60\cdot1.2^(24)\cong4770`

Therefore, rounding to the nearest whole number, the answer is 4770 viruses.