I need some help.
A biologist finds that the population of a certian type of bacteria double seach half-hour. An initial culture has 60 bacteria.
1. What is the population after 3 hours?
2. How long will it take for the number of bacteria to reach 983,040?
let number = 60 (2)^(2t) , where t is in hours
when t = 3
number = 60 (2)^6 = 3840
2. we would be solving
60 (2)^(2t) = 983040
2^(2t) = 16384 which just happens to be 2^14
so 2^2t = 2^14
2t = 14
t = 7 , it would take 7 years
it was probably a planned question, if not we would have had to use logarithms
Sure, I'd be happy to help you with those questions!
To answer them, we need to understand how the population of bacteria is changing over time. The problem states that the population doubles every half-hour. Using this information, we can calculate the population at different time intervals.
1. To find the population after 3 hours, we need to convert the given time into half-hour increments. Since each half-hour doubles the population, for 3 hours (6 half-hours), we would have:
Population after 3 hours = initial population (60 bacteria) * 2^(number of half-hours)
= 60 * 2^(6)
= 60 * 64
= 3840
Therefore, the population after 3 hours would be 3840 bacteria.
2. To determine how long it will take for the number of bacteria to reach 983,040, we need to find the number of half-hour intervals required. This can be calculated by taking the logarithm base 2 of the final population divided by the initial population:
Number of half-hours = log2(final population / initial population)
= log2(983040 / 60)
= log2(16384)
Using a logarithmic calculator, we find that log2(16384) = 14.
Therefore, it will take 14 half-hour intervals for the number of bacteria to reach 983,040.
I hope that helps! Let me know if there's anything else I can assist you with.