Problema Solution
a colony of bacteria is growing exponentially. At the end of 3 hours there are 1000 bacteria. At the end of 5 hours there are 3000 bacteria. Write a formula for the population of bacteria at time t, in hours. By what percent does the number of bacteria increase each hour?
Answer provided by our tutors
we use the following formula for exponential growth:
t = a(1+r)^x
where t = current total, a = initial amount, r = rate of growth and x=number of time intervals
we have time intervals expressed in hours, we do not know the initial amount and we do not now the rate of growth
1000 = a(1+r)^3
3000 = a(1+r)^5
solving this system we have:
a = 192.45
r = 0.7321
a formula for the population at time 't', in hours, where f(t) represents the bacteria population, is:
f(t) = 192.45(1.7321)^t