Question

Suppose a culture of bacteria starts with 9000 bacteria. After one hour, the count is 10,000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling time of the bacteria. Round the doubling time to the nearest 0.01 hours.

Answer 1

For each hour, the population increases by 10,000 / 9,000 or 1.111111111111111
Ending Amount = Beginning Amount * (1+rate)^time
Ending Amount = 9,000 * (1.11111111111111)^hours
Ending Amount = 9,000 * (1.11111111111111)^1 = 10,000
Ending Amount = 9,000 * (1.11111111111111)^2 = 11,111

To find the doubling time, we must make the equation:
18,000 = 9,000 * (1.11111111111111)^time

2 = (1.11111111111111)^time
taking logs of both sides
log(2) = time * log (1.1111111111)

time = log(2) / log (1.1111111111)

time = 0.3010299957 / 0.0457574906

time = 6.5788134796 hours

and to double check the calculations here's an online calculator:
http://www.1728.org/expgrwth.htm

Answer 2

thanks a lot!