a. Which interest rate and compounding period gives the best return? .8% compounded annually • 7.5% compounded semi-annually • 7% compounded continuously b. On a college campus of 5000 students, one student returns from a vacation with a contagious virus. 5000 The spread of the virus is modeled by: y a. After 5 days, how many students are infected? (1+4999 e(-.8t) b. Classes are cancelled when the number infected is 40% or more. How many days will it take for this number to be reached?
a. Which interest rate and compounding period gives the best return? .8% compounded annually • 7.5% compounded semi-annually • 7% compounded continuously b. On a college campus of 5000 students, one student returns from a vacation with a contagious virus. 5000 The spread of the virus is modeled by: y a. After 5 days, how many students are infected? (1+4999 e(-.8t) b. Classes are cancelled when the number infected is 40% or more. How many days will it take for this number to be reached?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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![**Mathematical Modeling and Compounding Interest - Educational Exercise**
**a. Interest Rate and Compounding Period Analysis**
Consider the following scenarios to determine which interest rate and compounding period gives the best return:
- 8% compounded annually
- 7.5% compounded semi-annually
- 7% compounded continuously
**b. Virus Spread on a College Campus**
Imagine a college campus with 5000 students. Suppose one student returns from a vacation carrying a contagious virus.
The spread of the virus is mathematically modeled by the equation:
\[ y = \frac{5000}{1 + 4999 \, e^{-0.8t}} \]
Consider the following questions:
1. **After 5 days, how many students are infected?**
2. **Classes are canceled when the number of infected students is 40% or more.**
*How many days will it take for this threshold to be reached?*
In this exercise, you will apply mathematical concepts to evaluate the optimal compounding interest scenario and predict the virus's spread on a college campus. Use exponential growth modeling and compounding interest formulas to solve these problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a328885-7641-4d6d-85af-435d99e02dcf%2F1ffcda64-f8c3-4d92-80ed-8bbe4e8adb7d%2Frixksh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematical Modeling and Compounding Interest - Educational Exercise**
**a. Interest Rate and Compounding Period Analysis**
Consider the following scenarios to determine which interest rate and compounding period gives the best return:
- 8% compounded annually
- 7.5% compounded semi-annually
- 7% compounded continuously
**b. Virus Spread on a College Campus**
Imagine a college campus with 5000 students. Suppose one student returns from a vacation carrying a contagious virus.
The spread of the virus is mathematically modeled by the equation:
\[ y = \frac{5000}{1 + 4999 \, e^{-0.8t}} \]
Consider the following questions:
1. **After 5 days, how many students are infected?**
2. **Classes are canceled when the number of infected students is 40% or more.**
*How many days will it take for this threshold to be reached?*
In this exercise, you will apply mathematical concepts to evaluate the optimal compounding interest scenario and predict the virus's spread on a college campus. Use exponential growth modeling and compounding interest formulas to solve these problems.
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