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Question 1 Let g(t) be the population (in thousands of people) of Calculus City, as a function the time t (in years), where t= 0 corresponds to the year 2020. In 2020, the population was 10000, and each year the population increases by 30%. (a) Model the population by finding a formula for g(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof. (b) Evaluate the expression g(6), and write a sentence explaining what this means. (c) Solve the equation g(t) = 16.9, and write a sentence explaining what this means.

Question 1 Let g(t) be the population (in thousands of people) of Calculus City, as a function the time t (in years), where t= 0 corresponds to the year 2020. In 2020, the population was 10000, and each year the population increases by 30%. (a) Model the population by finding a formula for g(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof. (b) Evaluate the expression g(6), and write a sentence explaining what this means. (c) Solve the equation g(t) = 16.9, and write a sentence explaining what this means.

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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assignments/14852683 df Math 140 Written Homework 2: 1.6-2.3 Page 1 of 2 Question 1 Let g(t) be the population (in thousands of people) of Calculus City, as a function the time t (in years), where t = 0 corresponds to the year 2020. In 2020, the population was 10000, and each year the population increases by 30%. (a) Model the population by finding a formula for g(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof. (b) Evaluate the expression g(6), and write a sentence explaining what this means. (c) Solve the equation g(t) = 16.9, and write a sentence explaining what this means. Question 2 Answer the following parts. (a) Write down a ormula for the amount of money you would have in your account after t years if it started at $1000 and the account pays 2.5% annual interest compounded monthly. (b) If you buy a car for $20,000 and it loses half its value every year when will the car be worth $3,000? (c) A population is known to grow exponentially. If it starts at 100 and is 150 after 3 months when will the population be 300? Question 3 Newton's Law of Cooling (which applies to warming as well) says that the temperature difference 4 between an object and its surroundings is an exponentially decaying function of time, provided that surrounding temperature remains constant. Suppose that the surrounding temperature does not depend on time, and denote this temperature T.. Let T(t) be the temperature of an object at time t. Translating "the temperature difference between an object and its surroundings is an exponentially decaying function of time" into an equation yields T(t)-T, = ae-kt where a and k are constants. (More specifically we know k> 0, otherwise the object temperature wouldn't approach the surrounding temperature in the long run.) Without too much trouble it can be deduced that Page < T(t)-T,= (To-T.)e-kt, where To is the temperature of the object at t = 0. A 98°C hard-boiled egg is put into a big pot of 18°C water at t= 0, where t is measured in minutes. After 5 minutes the temperature of the egg drops to 38°C. (a) Use the data above to solve for T(t), the temperature of the egg at time t. The only variable in your answer should be the input, t. (b) What is a realistic domain of the temperature function? (c) Draw a rough sketch of the function and label any intercepts and asymptotes. 1
Transcribed Image Text:assignments/14852683 df Math 140 Written Homework 2: 1.6-2.3 Page 1 of 2 Question 1 Let g(t) be the population (in thousands of people) of Calculus City, as a function the time t (in years), where t = 0 corresponds to the year 2020. In 2020, the population was 10000, and each year the population increases by 30%. (a) Model the population by finding a formula for g(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof. (b) Evaluate the expression g(6), and write a sentence explaining what this means. (c) Solve the equation g(t) = 16.9, and write a sentence explaining what this means. Question 2 Answer the following parts. (a) Write down a ormula for the amount of money you would have in your account after t years if it started at $1000 and the account pays 2.5% annual interest compounded monthly. (b) If you buy a car for $20,000 and it loses half its value every year when will the car be worth $3,000? (c) A population is known to grow exponentially. If it starts at 100 and is 150 after 3 months when will the population be 300? Question 3 Newton's Law of Cooling (which applies to warming as well) says that the temperature difference 4 between an object and its surroundings is an exponentially decaying function of time, provided that surrounding temperature remains constant. Suppose that the surrounding temperature does not depend on time, and denote this temperature T.. Let T(t) be the temperature of an object at time t. Translating "the temperature difference between an object and its surroundings is an exponentially decaying function of time" into an equation yields T(t)-T, = ae-kt where a and k are constants. (More specifically we know k> 0, otherwise the object temperature wouldn't approach the surrounding temperature in the long run.) Without too much trouble it can be deduced that Page < T(t)-T,= (To-T.)e-kt, where To is the temperature of the object at t = 0. A 98°C hard-boiled egg is put into a big pot of 18°C water at t= 0, where t is measured in minutes. After 5 minutes the temperature of the egg drops to 38°C. (a) Use the data above to solve for T(t), the temperature of the egg at time t. The only variable in your answer should be the input, t. (b) What is a realistic domain of the temperature function? (c) Draw a rough sketch of the function and label any intercepts and asymptotes. 1
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