**Educational Website Content****Title:** Calculation of Virus Spread Over Time**Description:**Understanding how a virus spreads through a population is crucial for controlling outbreaks. In mathematical terms, the rate at which a virus spreads can be represented by a specific function. Below, we explore a function that describes this rate and calculate the number of people infected over a given time period.**Mathematical Model:**The rate at which a virus spreads through a population (measured in people per day) is given by the function:\[ r(t) = 2.33e^{1.165t} \]where:- $ r(t) $ is the rate of infection (people per day)- $ t $ is the number of days since the initial infection**Problem Statement:**Calculate the number of people infected between days 7 and 14. Round your answer to the nearest person.**Detailed Explanation:**To find out how many people were infected between days 7 and 14, we need to integrate the given function $ r(t) $ from $ t = 7 $ to $ t = 14 $.**Steps:**1. Set up the integral to represent the total number of infections between days 7 and 14:\[ \int_{7}^{14} 2.33e^{1.165t} \, dt \]2. Solve the integral analytically:\[ \int 2.33e^{1.165t} \, dt = \frac{2.33}{1.165} e^{1.165t} + C \]\[ = 2.00 e^{1.165t} + C \]3. Evaluate the integral from $ t = 7 $ to $ t = 14 $:\[ \left[ 2.00 e^{1.165t} \right]_{7}^{14} = 2.00 e^{1.165 \cdot 14} - 2.00 e^{1.165 \cdot 7} \]4. Calculate the exponential values and subtract:\[ 2.00 e^{1.165 \cdot 14} - 2.00 e^{1.165 \cdot 7} \approx 2.00 (1235072.36) - 2.00 (518.02) \]\[ \approx 2470144 **How much work does it take this squirrel to suck all the beer out of one of these cylindrical cans?** *Note: The straw reaches 3 in out of the can, the can is 4.5 in tall with a diameter of 2.5 in. This beer weighs 0.036 lb/in³.*

The rate at which a virus spreads through a population (measured in people per day) is given by the function r(t) = 2.33e1.165t, where t is the number of days since the initial infection. How many people were infected between days 7 and 14? Round your answer to the nearest person.

The rate at which a virus spreads through a population (measured in people per day) is given by the function r(t) = 2.33e1.165t, where t is the number of days since the initial infection. How many people were infected between days 7 and 14? Round your answer to the nearest person.

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...

See similar textbooks

Related questions

Q: The efficiency E (in %) of an automobile engine is given by: E= 0.736 s-0.00005 s3 where s is the…

Q: find z a/2 for a=0.08

A: The zα/2 critical value of the standard normal distribution, is the value, above which, 100 (α/2) %…

Q: The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in…

Q: .02t The size of a certain insect population is given by P(t) = 300e where t is measured in days. At…

A: Given ,The size of a certain insect population is : We have to measure at what time will the…

Q: number

Q: Garrett planted some parsley seeds in his garden and has been measuring their weeks. Week 12 Height…

A: (a) Calculate the increase in growth of plants from week 1-2, week 2-3 and week 3-4. week 1-2…

Q: Suppose that the instantaneous rate of change of the untreated mosquitoes is 1204 at t=1, where t…

A: Let the population of untreated mosquitos be M(t). And, M(t) satisfies the equation dMtdt=kM, where…

Q: $2500 is deposited in an account with an interest rate of r% per year, compounded monthly. At the…

Q: If F = 0.85 and MSE = 86, what is MST equal to?

A: The total variation present in a set of observable quantities may, under certain circumstances, be…

Q: If the average test score (in percent) of a group of math students at IMU is given by p=100-5ln(3t…

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

**Educational Website Content**

**Title:** Calculation of Virus Spread Over Time

**Description:**
Understanding how a virus spreads through a population is crucial for controlling outbreaks. In mathematical terms, the rate at which a virus spreads can be represented by a specific function. Below, we explore a function that describes this rate and calculate the number of people infected over a given time period.

**Mathematical Model:**
The rate at which a virus spreads through a population (measured in people per day) is given by the function:

\[ r(t) = 2.33e^{1.165t} \]

where:
- $ r(t) $ is the rate of infection (people per day)
- $ t $ is the number of days since the initial infection

**Problem Statement:**
Calculate the number of people infected between days 7 and 14. Round your answer to the nearest person.

**Detailed Explanation:**
To find out how many people were infected between days 7 and 14, we need to integrate the given function $ r(t) $ from $ t = 7 $ to $ t = 14 $.

**Steps:**
1. Set up the integral to represent the total number of infections between days 7 and 14:

\[ \int_{7}^{14} 2.33e^{1.165t} \, dt \]

2. Solve the integral analytically:

\[ \int 2.33e^{1.165t} \, dt = \frac{2.33}{1.165} e^{1.165t} + C \]
\[ = 2.00 e^{1.165t} + C \]

3. Evaluate the integral from $ t = 7 $ to $ t = 14 $:

\[ \left[ 2.00 e^{1.165t} \right]_{7}^{14} = 2.00 e^{1.165 \cdot 14} - 2.00 e^{1.165 \cdot 7} \]

4. Calculate the exponential values and subtract:

\[ 2.00 e^{1.165 \cdot 14} - 2.00 e^{1.165 \cdot 7} \approx 2.00 (1235072.36) - 2.00 (518.02) \]
\[ \approx 2470144

**How much work does it take this squirrel to suck all the beer out of one of these cylindrical cans?**

*Note: The straw reaches 3 in out of the can, the can is 4.5 in tall with a diameter of 2.5 in. This beer weighs 0.036 lb/in³.*

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Final answer

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

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

Similar questions

The number of new chain saws sold t years after the introduction of a new model is givenby the function y= 2300 ln(8t+3). How many chain saws will be sold 5 years after thenew model is introduced? Round your answer to the nearest whole number.
A train with a maximum speed of 105 km/h has an acceleration rate of 0.67 m/s2and a deceleration rate of 0.77 m/s2. How long does it take for the train to accelerate to maximum speed from rest? Provide your answer in s and round to one decimal place
A population of bacteria is growing according to the equation P(t) = 1100e0.04t. In how many years will the population will exceed 1296? Round your answer to one decimal place. %3D t =
The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 300 bacteria are present. After 10 hours 4000 bacteria are present. What was the initial number of bacteria? (Round your answer to the nearest integer.) bacteria
A certain sport car can accelerate from a starting point to a speed of v(t) = -0.39t? + 13t where v is measured in metres per second. a. Find the distance that the car will travel in the first 4 seconds. Round to two decimal places if necessary b. Find the distance that the car will travel in the first 9 seconds. Round to two decimal places if necessary
Suppose the total income in dollars from a machine is given by the following. I= 10e0.5t, 0sts 6, tin hours Find the average income (in dollars) over this 6-hour period. (Round your answer to the nearest cent.) $