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1. The number of a certain type of bacteria increases continuously at a rate proportional to the number present. If there are 100 present at a given time and 300 present 5 hours later, how many bacteria will present after 10 hours from the initial time?

1. The number of a certain type of bacteria increases continuously at a rate proportional to the number present. If there are 100 present at a given time and 300 present 5 hours later, how many bacteria will present after 10 hours from the initial time?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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can you please help me with question 1 and 3
D 211020.pdf Open with EXERCISE 4 Solve the following problems. 1. The number of a certain type of bacteria increases continuously at a rate proportional to the number present. If there are 100 present at a given time and 300 present 5 hours later, how many bacteria will present after 10 hours from the initial time? 2. A mathematical model was built to predict the size of a city. This model assumed that the population grew at a rate proportional to the population present at time t and the city had a population of 15000 persons at the beginning of the year 2011. Estimate the population of the city at the beginning of the year 2018 if the constant of proportionality, k, is 0.05. 3. A virus spreads very rapidly. After 20 minutes, the number of the virus is found to be 175. After 1 hour the number increases to 986. Find the initial population of the virus and how long will it take for the number of the virus to become hundred times larger than its initial population? 4. The population of a freshwater fish in a pond is N. After three months, the population of the freshwater fish has tripled. How long will the population of the freshwater fish become five times larger than its initial population? 5. A population of rabbits is growing exponentially. At the beginning, there were 50 rabbits and 4 years later there were 1,500 rabbits. How long will it take for the population of rabbits to reach 200,000? 6. The growth rate of the population of Putrajaya is proportional to the current population. If Putrajaya had a population of 55,000 in 2006 and a population of 65,000 in year 2016, find an expression for the population at any time, t. 7. The total population of foreign workers in a town in the year 2005 was 50,000. After 5 years, the number of population has doubled. Calculate the time for the population to become five times larger than its initial population. 8. Bacteria grow in a nutrient solution at a rate proportional to the number present. If the number N increases fromage to 00 stralds in 7nourS when wil the bacteria reach 1,600? 9. The population of a towh grows at a rate proportional to the population present at time t. If the Go A 0 N 81°F 近
Transcribed Image Text:D 211020.pdf Open with EXERCISE 4 Solve the following problems. 1. The number of a certain type of bacteria increases continuously at a rate proportional to the number present. If there are 100 present at a given time and 300 present 5 hours later, how many bacteria will present after 10 hours from the initial time? 2. A mathematical model was built to predict the size of a city. This model assumed that the population grew at a rate proportional to the population present at time t and the city had a population of 15000 persons at the beginning of the year 2011. Estimate the population of the city at the beginning of the year 2018 if the constant of proportionality, k, is 0.05. 3. A virus spreads very rapidly. After 20 minutes, the number of the virus is found to be 175. After 1 hour the number increases to 986. Find the initial population of the virus and how long will it take for the number of the virus to become hundred times larger than its initial population? 4. The population of a freshwater fish in a pond is N. After three months, the population of the freshwater fish has tripled. How long will the population of the freshwater fish become five times larger than its initial population? 5. A population of rabbits is growing exponentially. At the beginning, there were 50 rabbits and 4 years later there were 1,500 rabbits. How long will it take for the population of rabbits to reach 200,000? 6. The growth rate of the population of Putrajaya is proportional to the current population. If Putrajaya had a population of 55,000 in 2006 and a population of 65,000 in year 2016, find an expression for the population at any time, t. 7. The total population of foreign workers in a town in the year 2005 was 50,000. After 5 years, the number of population has doubled. Calculate the time for the population to become five times larger than its initial population. 8. Bacteria grow in a nutrient solution at a rate proportional to the number present. If the number N increases fromage to 00 stralds in 7nourS when wil the bacteria reach 1,600? 9. The population of a towh grows at a rate proportional to the population present at time t. If the Go A 0 N 81°F 近
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