Question

In: Advanced Math

(1 point) A bacteria culture starts with 560 bacteria and grows at a rate proportional to...

(1 point) A bacteria culture starts with 560 bacteria and grows at a rate proportional to its size. After 3 hours there will be 1680 bacteria.

(a) Express the population after t hours as a function of t
population:  (function of t)

(b) What will be the population after 2 hours?


(c) How long will it take for the population to reach 1250 ?

Solutions

Expert Solution

In lastly. To get the time first we do 1250÷560 and get a fraction . Then we multiply bye 60. As 1 hours =60 min. Then we get some  minutes and fraction. Then similarly multiply by 60 as 1 minute =60 second.


Related Solutions

USE PYTHON TO SOLVE THIS PROBLEM A bacteria culture grows exponentially. After 2 hours, the bacteria...
USE PYTHON TO SOLVE THIS PROBLEM A bacteria culture grows exponentially. After 2 hours, the bacteria count was 400 cells and after 6 hours, the bacteria count was 20,000 cells. a) Solve a system of equations to find (approximately) k and y0 (HINT: If will help to assume K is real in the symbols command) b) Use this to determine when the bacteria count reaches 2,000,000 (exact and approximate). c) Suppose 400 was the “initial” amount and 20,000 the count...
USE PYTHON TO SOLVE THIS PROBLEM A bacteria culture grows exponentially. After 2 hours, the bacteria...
USE PYTHON TO SOLVE THIS PROBLEM A bacteria culture grows exponentially. After 2 hours, the bacteria count was 400 cells and after 6 hours, the bacteria count was 10,000 cells. a) Solve a system of equations to find (approximately) k and y0 (HINT: If will help to assume K is real in the symbols command) b) Use this to determine when the bacteria count reaches 1,000,000 (exact and approximate). c) Suppose 400 was the “initial” amount and 10,000 the count...
(1 point) The count in a bacteria culture was 200 after 15 minutes and 557 after...
(1 point) The count in a bacteria culture was 200 after 15 minutes and 557 after 25 minutes. Assume the growth can be modelled exponentially by a function of the form Q(t)=A e rt Q(t)=Aert , where t t is in minutes. (a) Find the relative growth rate, with at least the first 5 digits after the decimal point entered correctly: r= r= equation editor Equation Editor (b) What was the initial size of the culture? Round your answer to...
(1 point) The count in a bacteria culture was 600 after 10 minutes and 11613 after...
(1 point) The count in a bacteria culture was 600 after 10 minutes and 11613 after 20 minutes. Assume the growth can be modelled exponentially by a function of the form Q(t)=AertQ(t)=Aert, where tt is in minutes. (a) Find the relative growth rate, with at least the first 5 digits after the decimal point entered correctly: r=r= equation editor Equation Editor (b) What was the initial size of the culture? Round your answer to the closest integer. equation editor Equation...
2. The growth rate of a population of bacteria is directly proportional to the population p(t)...
2. The growth rate of a population of bacteria is directly proportional to the population p(t) (measured in millions) at time t (measured in hours). (a) Model this situation using a differential equation. (b) Find the general solution to the differential equation. (c) If the number of bacteria in the culture grew from p(0) = 200 to p(24) = 800 in 24 hours, what was the population after the first 12 hours? 3. Find the particular solution y(x) to the...
1. There are 300 bacteria in a culture, and the number of bacteria quadruples every 5...
1. There are 300 bacteria in a culture, and the number of bacteria quadruples every 5 hours. A. Write a function, N, that gives the number of bacteria t hours from now. B. How many will there be in 20 hours? C. In how many hours will there be 2,000 bacteria? 2. The population of Johnsonville was 900 in 1880 and is known to double every 20 years. a. Write a function, P, that gives the population y years after...
(1 point) Bacteria grow at a rate of 27% per hour in a petri dish. If...
(1 point) Bacteria grow at a rate of 27% per hour in a petri dish. If there are initially 100 bacteria and a carrying capacity of 500000 cells, how long does it take to reach 94000 cells? t = _____ hours
point) The count in a bacteria culture was 500 after 10 minutes and 32518 after 30...
point) The count in a bacteria culture was 500 after 10 minutes and 32518 after 30 minutes. Assume the growth can be modelled exponentially by a function of the form Q(t)=A e rt Q(t)=Aert , where t t is in minutes. (a) Find the relative growth rate, with at least the first 5 digits after the decimal point entered correctly: r= r= equation editor Equation Editor (b) What was the initial size of the culture? Round your answer to the...
1. A tank starts with 100 litres of water and 1,000 bacteria in it. For now...
1. A tank starts with 100 litres of water and 1,000 bacteria in it. For now we assume the bacteria do not reproduce. Let B(t) be the number of bacteria in the tank as a function of time, where t is in hours. For each of the situations below, write down a first order differential equation satisfied by B(t), of the form dB dt = f(t, B). You DO NOT need to solve it. (a) A little goblin is pouring...
a) Suppose that 650 bacteria are present initially in a culture. If the number of bacteria...
a) Suppose that 650 bacteria are present initially in a culture. If the number of bacteria triple every 5 hours, how long is it until there are 50,000 bacteria in the culture? b) The half-life of C14 is 5730 years. If a fossilized leaf contains 42% of its normal amount of C14, how old is the fossil? c) HOw long does it take for an investment to double in value if it is invested at 3.6% compounded quarterly?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT