(a) In a certain culture of bacteria the rate of increase is proportional to the numberpresent.(i) If it is found that the number doubles in 8 hours, how many may be expeetedat the end of 24 hours?(ii) If there are 10* at the end of 7 hours and 4 x 10* at the end of 9 hours, howmany were there in the beginning?(b) According to Newton's law of cooling, the rate at which a substance cools inmoving air is proportional to the difference between the temperature of the substanceand that of the air. If the temperature of the air is 32 and the substance cools from100 to 70° in 15 minutes, find when the temperature will be 12°.

Since you have posted a multiple question ,I will solve the first question for you. To get…

(a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i) If it is found that the number doubles in 8 hours, how many may be expected at the end of 24 hours? (ii) If there are 10* at the end of 7 hours and 4 x 10* at the end of 9 hours, how many were there in the beginning?

(a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i) If it is found that the number doubles in 8 hours, how many may be expected at the end of 24 hours? (ii) If there are 10* at the end of 7 hours and 4 x 10* at the end of 9 hours, how many were there in the beginning?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Suppose that in a certain area the consumption of electricity has increased at a continuous rate of…

A: topic- exponential function

Q: Suppose that poaching reduces the population of an endangered animal by 4% per year. Further suppose…

A: Initial population = A = 1500 r = 0.04 P = 70 Model : P = A(1-r)t

Q: L{ - 2)н( — 3)}

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: what happens if we have a situation of a rate of approximately 2 diepers change every 0.9 hour?

Q: The following is an excerpt from the U.S. Census report, “The Older Population: 2010”: “Between 2000…

Q: An experimental forest is to be grown by planting 3000 trees each year on the same day of the year.…

A: Let i = number of years = 0, 1, ... , 10 and the number of trees planting in the starting of each…

Q: The effective reproductive number (Re) can be defined as the average number of new infections caused…

A: Given for a highly virulent disease the basic reproductive number is R0=3 and the population immune…

Q: What rate is required to grow 100 to 10,000 in 10 years?

Q: 00 E (-1)n+1_1 n=1 1.23 x 10-2 4.12 x 10-3 1.37 x 10-3

Q: 77. Simple epidemic. An influenza epidemic has spread throughout a community of 50,000 people at a…

A: Total population =50,000Let y be number of people infected then 50,000-y non infected people

Q: Suppose that the initial population of deer in a state is 5,000 and is growing 6% each year. Which…

A: Formula used of compound interest A = p(1+r/n)^(nt) where A is total amount after interest r is…

Q: If the population of a country doubles in 90 years, in how many years will it treble under the…

Q: Suppose the population of certain fungi in a laboratory sample is 12. (A) If it quintuples in…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Percentage : Percentage of the item is 100th part of the number. It is denoted by x% or written as…

Q: ও 1000

A: 6) Consider the given sequence an=n+12n1-1n It can be written as an=n+12nn-1n ⇒an=n2-12n2 A…

Q: Example 42. A train travels first 300 kilometres at an average rate of 30 k.p.h. and further travels…

Q: A population of termites doubles every 0.35 days. The initial population is 1800 termites. a) How…

Q: 25 5.²5 4 Incx √x dx

Q: 2. Suppose that a bacteria population is dying off at a rate of 30% per day. How much of the…

Q: A total of 1,500 bacteria were present at the start of an experiment. These bacteria were placed…

A: The growth or decay is modelled using the equation, f(t)=a1±rt. Here, a is the initial population, r…

Q: 1/4 = n/100 what is n?

Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

Q: Suppose that the population of whales in world’s oceans increases by 20 % per year in the absence of…

Q: What is the value of E(X-1)^2 for the scores 1,3, and 4? 49 12 13 30

A: We have to find sum of (x-1)2

Question

(a) In a certain culture of bacteria the rate of increase is proportional to the number
present.
(i) If it is found that the number doubles in 8 hours, how many may be expeeted
at the end of 24 hours?
(ii) If there are 10* at the end of 7 hours and 4 x 10* at the end of 9 hours, how
many were there in the beginning?
(b) According to Newton's law of cooling, the rate at which a substance cools in
moving air is proportional to the difference between the temperature of the substance
and that of the air. If the temperature of the air is 32 and the substance cools from
100 to 70° in 15 minutes, find when the temperature will be 12°.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

229 25. Researchers have observed that rainforest areas next to clear-cuts (less than 100 meters away) have a reduced tree biomass compared to rain- forest areas far from clear-cuts. To go further, Laurance et al. (1997) tested whether rainforest areas more distant from the clear-cuts were also affected. They compiled data on the biomass change after clear-cutting (in tons/hectare/year) for 36 rainforest areas between 100 m and sev- eral kilometers from clear-cuts. The data are as follows: -10.8, -4.9, -2.6, -1.6, -3, -6.2, -6.5, -9.2, -3.6,-1.8, -1.0, 0.2, 0.2, 0.1, -0.3, -1.4, -1.5, -0.8, 0.3, 0.6, 1.0, 1.2, 2.9, 3.5, 4.3, 4.7, 2.9, 2.8, 2.5, 1.7, 2.7, 1.2, 0.1, 1.3, 2.3, 0.5. These measurements are plotted in the following histogram: Frequency 14- 12- 10- 8- 64 2 0 -12.5 -10 -7.5 -5 -2.5 0 2.5 5 Biomass change Test whether there is a change in biomass of rain- forest areas following clear-cutting. hite the voragious habitat
Suppose the relationship between Y and X is given by: Y = 50 + 3X + error By how much does the expected value of Y change if X decreases by 2 units?
If a city's population is 1.3 million now and will grow at a continuous rate of 4.5% in the future, what will the city's population be in the year 2030? Give your answer in millions of people with two places of accuracy to the right of the decimal.
27) A particular bacterium is found to have a doubling time of 20 minutes. If a laboratory culture begins with a population of 300 of this bacteria and there is no change in the growth rate, how many bacteria will be present in 55 minutes? Use six decimal places in the interim calculation for the growth rate.
The population of certain species of bats doubles every five hours, initially there are 40 bats (a) Estimate the bats population after 20 hours. (b) When will the bats population reach 20000?
Q1. Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In certain sample 10% of the original number of radioactive nuclei have undergone disintegration in a period of 100 years. a) What percentage of the original radioactive nuclei will remain after 1000 years? b) In how many years will only one-fourth (1/4) of the original number remain?
Suppose the relationship between Y and X is given by: Y = 25 - 3X + error By how much does the expected value of Y change if X decreases by 2 units?