If the number of bacteria in a colony triples every 60 minutes and the population is currently 2,000 bacteria, what will the population be in 240 minutes? Is the growth modeled by a linear function or an exponential function?
Question
If the number of bacteria in a colony triples every 60 minutes and the population is currently 2,000 bacteria, what will the population be in 240 minutes? Is the growth modeled by a linear function or an exponential function?
Solution
The growth of the bacteria is an example of exponential growth because the population triples every 60 minutes.
Here's how you can calculate the population after 240 minutes:
-
First, determine how many 60-minute periods are in 240 minutes. This is done by dividing 240 by 60. The result is 4 periods.
-
Since the population triples every period, you raise 3 (the growth rate) to the power of 4 (the number of periods). 3^4 equals 81.
-
Finally, multiply the current population by the growth factor to find the future population. 2000 bacteria * 81 equals 162,000 bacteria.
So, the population will be 162,000 bacteria in 240 minutes. The growth is modeled by an exponential function, not a linear function, because the rate of growth is proportional to the current population.
Similar Questions
nstructions: Determine whether the following situation can be modeled by a linear or exponential relationship, and use the model to answer the question.If the number of bacteria in a colony triples every 60 minutes and the population is currently 3,000 bacteria, what will the population be in 240 minutes? Is the growth modeled by a linear function or an exponential function?The population will be Answer 1 Question 12 and it is modeled by a Answer 2 Question 12
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 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
A bacterial population is exponentially growing at a growth rate of 0.1 per individual per hour. The initial population size is 1. Assume that 𝑙𝑜𝑔10(𝑒)=0.5. How many hours does it take for the population size to reach 1000? See if you can answer this question without using a calculator or computer.Group of answer choices1998069.0782300260
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
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.