Final answer:
Maria will find 480 viruses after 15 hours, calculated using the exponential growth formula N = N0 × (1 + r)^t with an initial quantity of 100 viruses and a growth rate of 17% per hour.
Step-by-step explanation:
The student's question involves finding how many viruses Maria will observe after 15 hours if she starts with 100 viruses that grow at a rate of 17% per hour. This is a clear example of exponential growth, a concept commonly seen in populations of organisms like bacteria or viruses, where the number of individuals increases at a rate proportional to the current population size. To solve this problem, we can use the formula for exponential growth:
N = N0 × (1 + r)t
Where:
- N is the final number of viruses
- N0 is the initial number of viruses (100 in this case)
- r is the growth rate per unit time (0.17 or 17% per hour)
- t is the total time in hours (15 hours)
By substituting the given values into the formula:
N = 100 × (1 + 0.17)15
After carrying out the calculations:
N = 100 × (1.17)15
N = 100 × 4.80
N = 480
Therefore, Maria will observe 480 viruses after 15 hours.
However, this calculation is based on a simplified model of virus growth that might not account for complex factors such as resource limitations, immune response, or other environmental factors that could influence the actual growth rate of the virus.