1. Exponential functions and their graphs. Know all the rules for restrictions on the variables, points on the graph, asymptotes, domains, ranges, and to sketch the graphs and any transformations. a) Consider the graph (x) = c* . Sketch two graphs, one if 01. Give the coordinates of two points on each graph, and then give the range, domain, and equation of the horizontal asymptote of each. Also, tell me the restrictions on c. b) On separate axes, graph y-3", y-3**' +1, y = -3' , and y=2•3' . On each graph after the first one, give the coordinates of the two points after the transformations that started at (0,1) and (0,3) on the first graph. 2. The natural exponential function- S(x) = e" a) Sketch the graph of S(x) = e b) You all keep asking about a compound interest problem. The formula is simply A() = Pe" , were 4(1) is the amount of money you have after years if you put P dollars (principal) in the bank at a yearly interest rate of rper cent (expressed as a decimal). Following example 4 on page 341 in your book, and using your calculator, answer the following two questions. i. If you put $5000 in the bank at 4%log form, how much will you have after 6 years? If you put $5000 in the bank at 4% how long will it take you to double your money?
1. Exponential functions and their graphs. Know all the rules for restrictions on the variables, points on the graph, asymptotes, domains, ranges, and to sketch the graphs and any transformations. a) Consider the graph (x) = c* . Sketch two graphs, one if 01. Give the coordinates of two points on each graph, and then give the range, domain, and equation of the horizontal asymptote of each. Also, tell me the restrictions on c. b) On separate axes, graph y-3", y-3**' +1, y = -3' , and y=2•3' . On each graph after the first one, give the coordinates of the two points after the transformations that started at (0,1) and (0,3) on the first graph. 2. The natural exponential function- S(x) = e" a) Sketch the graph of S(x) = e b) You all keep asking about a compound interest problem. The formula is simply A() = Pe" , were 4(1) is the amount of money you have after years if you put P dollars (principal) in the bank at a yearly interest rate of rper cent (expressed as a decimal). Following example 4 on page 341 in your book, and using your calculator, answer the following two questions. i. If you put $5000 in the bank at 4%log form, how much will you have after 6 years? If you put $5000 in the bank at 4% how long will it take you to double your money?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you please help solve the attached questions
Transcribed Image Text:1. Exponential functions and their graphs. Know all the rules for restrictions on the variables,
points on the graph, asymptotes, domains, ranges, and to sketch the graphs and any
transformations.
a) Consider the graph f(x) = c* . Sketch two graphs, one if 0<c<1, and the other if c>1.
Give the coordinates of two points on each graph, and then give the range, domain, and
equation of the horizontal asymptote of each. Also, tell me the restrictions on c.
b) On separate axes, graph y = 3", y = 3** +1, y=-3" , and y=2•3* . On each graph after
the first one, give the coordinates of the two points after the transformations that
started at (0,1) and (1,3) on the first graph.
2. The natural exponential function- S(x) = e*
a) Sketch the graph of f(x) = e*
b) You all keep asking about a compound interest problem. The formula is simply
A(t) = Pe" , were 4(1) is the amount of money you have after ' years if you put P dollars
(principal) in the bank at a yearly interest rate of r per cent (expressed as a decimal).
Following example 4 on page 341 in your book, and using your calculator, answer the
following two questions.
i.
If you put $5000 in the bank at 4%log form, how much will you have after 6 years?
ii.
If you put $5000 in the bank at 4% how long will it take you to double your money?
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