Tv Tv □ v OV Tool Comment & Markup Management Kdan Cloud Share 4 Curve sketching, Optimization and Ap... Edit + A= Outlines Q Search ►Further uses of functions of... Solutions 186% T Annotation FAX OCR Q Editor OCR Convert Fax Search (C) What is the matme Hatical name given to the function √2 113. Assume that f(1) = 2.5, f'(1) = 0.5 and ƒ"(1) = -0.25. Use this information to estimate f(1.8). 114. If a country has a yearly inflation of 1% per year, the prices increase by i% every year. (For simplicity, we will assume here that the prices of all products increase by the same amount.) Sometimes it is said that the purchasing power then decreases by 1% per year. This means that the quantity of a certain product that one can buy for a given amount decreases by 1% per year. In this exercise, we show that this is not entirely correct. A certain good costs 10 €/kg. The inflation is 25% per year. We represent the time (in years, starting from now) by t and the price per kg of the good by p. (a) Write p as a function of t. We represent by A the amount (in kg) of the product that can be bought for €100. (b) Write A as a function of t. (c) Find the growth factor of the exponential growth process A(t). (d) By what percentage does A decrease every year? Now we assume that inflation is i% per year. (e) Show that in this case the purchasing power decreases exponentially and that the yearly growth factor is equal to 1+100 (f) Use this to show that the purchasing power decreases by q% every year, where q = (g) Find this percentage for the following values of i: 100, 10, 1 and 0.1. 100i 100+i' (h) Show that the purchasing power decreases by approximately 1% per year when the yearly inflation is very small. 115. At this moment, a website has 10 000 users and this number is growing at a rate of 2000 users per month. This growth rate is increasing: in a month's time, the growth rate is expected to be 3000 users per month. Use this information to find a function that approximates the number of users N in the near future, i.e., t months from now (where t is small). What is the mathematical name of this approximating function? 8 /11
Tv Tv □ v OV Tool Comment & Markup Management Kdan Cloud Share 4 Curve sketching, Optimization and Ap... Edit + A= Outlines Q Search ►Further uses of functions of... Solutions 186% T Annotation FAX OCR Q Editor OCR Convert Fax Search (C) What is the matme Hatical name given to the function √2 113. Assume that f(1) = 2.5, f'(1) = 0.5 and ƒ"(1) = -0.25. Use this information to estimate f(1.8). 114. If a country has a yearly inflation of 1% per year, the prices increase by i% every year. (For simplicity, we will assume here that the prices of all products increase by the same amount.) Sometimes it is said that the purchasing power then decreases by 1% per year. This means that the quantity of a certain product that one can buy for a given amount decreases by 1% per year. In this exercise, we show that this is not entirely correct. A certain good costs 10 €/kg. The inflation is 25% per year. We represent the time (in years, starting from now) by t and the price per kg of the good by p. (a) Write p as a function of t. We represent by A the amount (in kg) of the product that can be bought for €100. (b) Write A as a function of t. (c) Find the growth factor of the exponential growth process A(t). (d) By what percentage does A decrease every year? Now we assume that inflation is i% per year. (e) Show that in this case the purchasing power decreases exponentially and that the yearly growth factor is equal to 1+100 (f) Use this to show that the purchasing power decreases by q% every year, where q = (g) Find this percentage for the following values of i: 100, 10, 1 and 0.1. 100i 100+i' (h) Show that the purchasing power decreases by approximately 1% per year when the yearly inflation is very small. 115. At this moment, a website has 10 000 users and this number is growing at a rate of 2000 users per month. This growth rate is increasing: in a month's time, the growth rate is expected to be 3000 users per month. Use this information to find a function that approximates the number of users N in the near future, i.e., t months from now (where t is small). What is the mathematical name of this approximating function? 8 /11
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
100%
114 whole please
Transcribed Image Text:Tv Tv □ v OV
Tool
Comment & Markup
Management Kdan Cloud
Share
4 Curve sketching, Optimization and Ap... Edit +
A=
Outlines
Q Search
►Further uses of functions of...
Solutions
186%
T
Annotation
FAX
OCR
Q
Editor
OCR
Convert
Fax
Search
(C) What is the matme Hatical name given to the function √2
113. Assume that f(1) = 2.5, f'(1) = 0.5 and ƒ"(1) = -0.25. Use this information to estimate f(1.8).
114. If a country has a yearly inflation of 1% per year, the prices increase by i% every year. (For simplicity,
we will assume here that the prices of all products increase by the same amount.) Sometimes it is said
that the purchasing power then decreases by 1% per year. This means that the quantity of a certain
product that one can buy for a given amount decreases by 1% per year. In this exercise, we show that
this is not entirely correct.
A certain good costs 10 €/kg. The inflation is 25% per year. We represent the time (in years, starting
from now) by t and the price per kg of the good by p.
(a) Write p as a function of t.
We represent by A the amount (in kg) of the product that can be bought for €100.
(b) Write A as a function of t.
(c) Find the growth factor of the exponential growth process A(t).
(d) By what percentage does A decrease every year?
Now we assume that inflation is i% per year.
(e) Show that in this case the purchasing power decreases exponentially and that the yearly growth
factor is equal to
1+100
(f) Use this to show that the purchasing power decreases by q% every year, where q =
(g) Find this percentage for the following values of i: 100, 10, 1 and 0.1.
100i
100+i'
(h) Show that the purchasing power decreases by approximately 1% per year when the yearly inflation
is very small.
115. At this moment, a website has 10 000 users and this number is growing at a rate of 2000 users per
month. This growth rate is increasing: in a month's time, the growth rate is expected to be 3000 users
per month. Use this information to find a function that approximates the number of users N in the near
future, i.e., t months from now (where t is small). What is the mathematical name of this approximating
function?
8
/11
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