Bacteria are growing in a culture, and their number is increasing at the rate of 6% per hour. Initially, 200 bacteria are present.Determine an equation that gives the number
Question
Bacteria are growing in a culture, and their number is increasing at the rate of 6% per hour. Initially, 200 bacteria are present.Determine an equation that gives the number
Solution
The situation described is a classic example of exponential growth, which can be modeled by the equation:
N(t) = N0 * e^(rt)
where:
- N(t) is the number of bacteria at time t,
- N0 is the initial number of bacteria,
- r is the growth rate, and
- t is the time.
Given that the initial number of bacteria N0 is 200 and the growth rate r is 6% per hour (or 0.06 in decimal form), the equation becomes:
N(t) = 200 * e^(0.06t)
This equation gives the number of bacteria at any time t.
Similar Questions
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.(a) Find an expression for the number of bacteria after t hours.P(t) = 100·4.2t (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.)P(4) = bacteria(c) Find the rate of growth after 4 hours. (Round your answer to the nearest whole number.)P'(4) = bacteria per hour(d) When will the population reach 10,000? (Round your answer to one decimal place.)t = hr
A bacteria population is 7000 at time t = 0 and its rate of growth is 1000 · 2t bacteria per hour after t hours. What is the population after one hour? (Round your answer to the nearest whole number.)
In a lab experiment, a population of 100 bacteria is able to quadruple every hour. Which equation matches the number of bacteria in the population after 4 hours?Answer
a) A population of bacteria has an initial size 200. After one hour, the population has reached 220. The population grows in such a way that the rate of growth doubles each hour.(2 marks)i. What is the population after five hours? ii. Write a recurrence relation for growth of bacteria, be, after n hours. (3 marks)
A bacteria culture contains 1400 bacteria initially and doubles every hour.(a) Find a function N that models the number of bacteria after t hours.N(t) = (b) Find the number of bacteria after 24 hours. bacteria
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.