e) Let's see if we can understand WHY option B grows so much faster. Let's focus just on options A and B. Take a look at the data tables given for each function. Just the later parts of the initial table are provided. B(t) = .01(2) A(t) = 1000t + 1000 A(t)= t = t = B(t) = time in # of days 20 $ in account after t days 21,000 time in # of days 20 $ in account after t days 10,485.76
e) Let's see if we can understand WHY option B grows so much faster. Let's focus just on options A and B. Take a look at the data tables given for each function. Just the later parts of the initial table are provided. B(t) = .01(2) A(t) = 1000t + 1000 A(t)= t = t = B(t) = time in # of days 20 $ in account after t days 21,000 time in # of days 20 $ in account after t days 10,485.76
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Exponential and linear part 4
Transcribed Image Text:Lesson 3a - Introduction to Exponential Functions
MAT12x
e) Let's see if we can understand WHY option B grows so much faster. Let's focus just on options A and B.
Take a look at the data tables given for each function. Just the later parts of the initial table are provided.
B(t) = .01(2)
A(t) = 1000t + 1000
A(t)=
t =
t =
B(t)
time in # of days
$ in account after t days
time in # of days
$ in account after t days
20
21,000
20
10,485.76
21
22,000
21
20,971.52
22
23,000
22
41,943.04
23
24,000
23
83,886.08
24
25,000
24
167,772.16
25
26,000
25
335,544.32
26
27,000
26
671,088.64
27
28,000
27
1,342,177.28
28
29,000
28
2,684,354.56
29
30,000
29
5,368,709.12
30
30
10,737,418.24
31,000
32,000
31
31
21,474,836.48
As t increases from day 20 to 21, describe how the outputs change for each function:
A(t):
B(t):
As t increases from day 23 to 24, describe how the outputs change for each function:
A(t):
B(t):
So, in general, we can say as the inputs increase from one day to the next, then the outputs for each
function:
A(t):
B(t):
In other words, A(t) grows
and B(t) grows
We have just
identified the primary difference between LINEAR FUNCTIONS and EXPONENTIAL FUNCTIONS.
Exponential Functions vs. Linear Functions
The outputs for Linear functions change by ADDITION and the outputs for Exponential Functions change by
MULTIPLICATION.
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