Answer :
To estimate the number of bacteria after 15 minutes, we need to understand the rate of growth. Given that the initial number is 2000 and after 10 minutes it's 3000, this suggests a growth rate that can be modeled using exponential growth. This is a common scenario in bacterial growth calculations.
Let's assume the growth is exponential. We can use the formula N = N0*ert, where N is the final population size, N0 is the initial population size, r is the growth rate, and t is the time in the same units used for the growth rate. Since we don't have the growth rate, we need to find it using the information given (2000 bacteria growing to 3000 in 10 minutes). After finding 'r', we can use it to calculate the population after 15 minutes.
First, find 'r' using the available data:
- 3000 = 2000*e10r
- 1.5 = e10r
- ln(1.5) = 10r
- r = ln(1.5) / 10
Once 'r' is known, we can calculate the estimated number of bacteria after 15 minutes:
- N = 2000*e(ln(1.5)/10)*15
We can perform the calculation to find the estimated bacteria after 15 minutes.
