Question #30 56 Chapter 1 Modeling with Functions30. In Example 2, we modeled the population size (inmillions) of the United States as N(t) = 8.3(1.33)c. Evaluate this expression for larger and larger nand estimate the value it appears to be approach-ing.where t is measured in decades after 1815. Plot thisfunction over a fifty-year period and estimate thetime at which the population would triple in size.How does this compare to the actual time that thepopulation tripled in size?35. The following functions give the population sizeP(t) in millions for four fictional countries wheret is the number of decades since 1900.Country 1: P(t) = 3(1.5)'31. Consider $100 in a bank account that has annualinterest rate of 20%.Country 2: P2(t) = 10(1.1)'Country 3: P3(t) = 20(0.95)'a. Compute the amount in the bank account oneyear later if the money is compounded once ayear, twice a year, and four times a year.Country 4: P4(t) = 2(1.4)'a. Which country had the largest population size inb. Find an expression for the amount of money inthe bank account if the money is compounded ntimes a year.1900?b. Which country has the fastest population growthrate? By what percentage does this populationc. Evaluate this expression for larger and larger nand estimate the value it appears to be approach-ing.grow every decade?c. Is any of these populations decreasing in size?If so, which one and by what fraction does thepopulation size decrease every decade?32. Consider $1,000 in a bank account that has annualinterest rate of 5%.a. Compute the amount in the bank account oneyear later if the money is compounded once ayear, twice a year, and four times a year.36. The following functions give the froth height (in cen-timeters) of three fictional beers where t representstime (in seconds).Вeer 1: H (t) — 20(0.99)'b. Find an expression for the amount of money inthe bank account if the money is compounded ntimes a year.Вeer 2: H-(t) — 40 (0.9)'Beer 3: H3 (t) = 15(0.98)c. Evaluate this expression for larger and larger nand estimate the value it appears to be approach-ing.a. Which beer has the highest froth initially? Whatis the height?33. Consider a bacterial species that produces ten off-spring per day. Assume that you start with one bac-b. Which beer has the slowest decay of froth? Forthis beer, what percentage of the height is lost inten seconds? Twenty seconds?

The solution of above question no. #30 is written below with graph.

In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)' where t is measured in decades after 1815. Plot this function over a fifty-year period and estimate the time at which the population would triple in size. How does this compare to the actual time that the population tripled in size?

In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)' where t is measured in decades after 1815. Plot this function over a fifty-year period and estimate the time at which the population would triple in size. How does this compare to the actual time that the population tripled in size?

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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