partial growth factors ii
Module 4 : Investigation 5
MAT 170 | Precalculus
September 30, 2016
questions 1 & 2
Let f(x) = 9.5(1.24)x .
Let g(x) = 0.46(0.874)4x .
Determine the following :
Determine the following :
(a) 21 -unit growth factor :
(a) 41 -unit decay factor :
(b) 2-unit growth factor :
(b) 1-unit decay factor :
(c) 2-unit percent change :
(c) 5-unit percent change :
(d) Initial value :
(d) Initial value :
2
questions 1 & 2 - solutions
Let f(x) = 9.5(1.24)x .
Determine the following :
(a) 21 -unit growth factor : (1.24)1/2
(b) 2-unit growth factor : (1.24)2
(
)
(c) 2-unit percent change : 100 (1.24)2 − 1
(d) Initial value : 9.5
3
questions 1 & 2 - solutions
Let g(x) = 0.46(0.874)4x .
Determine the following :
(a) 41 -unit decay factor : 0.874
(b) 1-unit decay factor : (0.874)4
(
)
(c) 5-unit percent change : 100 (0.874)20 − 1
(d) Initial value : 0.46
4
question 4
Use the table below to determine the following values.
x
g(x)
1
260
4
278.2
7
297.674
10
318.511
(a) 3-unit growth/decay factor :
(c) 6-unit percent change :factor :
(d) 1-unit growth/decay factor :
(e) 41 -unit growth/decay factor :
(f) Initial value :
(g) Function :
5
question 4 - solutions
Use the table below to determine the following values.
x
g(x)
1
260
4
278.2
7
297.674
10
318.511
278.2
260
318.511
= 297.674
= 297.674
278.2
)
((
)2
−
1
(c) 6-unit percent change :factor : 100 278.2
260
(a) 3-unit growth/decay factor :
(d) 1-unit growth/decay factor :
( 278.2 )1/3
(e) 41 -unit growth/decay factor :
(f) Initial value : g(0) =
g(1)
1/3
( 278.2
260 )
260
≈ 1.0228
( 278.2 )1/12
260
=
260
1/3
( 278.2
260 )
≈ 254.2019
(g) Function : g(x) = 254.2019(1.0228)x
6
question 5
Below is the graph of f(x). Use the graph to determine the following
values.
(a) 2-unit growth/decay factor :
(b) 6-unit growth/decay factor :
(c) 1-unit percent change :
(d) 21 -unit growth/decay factor :
(e) 3-unit growth decay factor :
(f) Initial value :
(g) Function :
7
question 5 - solutions
Below is the graph of f(x). Use the graph to determine the following
values.
40
15.625
(a) 2-unit growth/decay factor :
( 40 )3
(b) 6-unit growth/decay factor : 15.625
)
((
)1/2
40
−1
(c) 1-unit percent change : 100 15.625
(d) 21 -unit growth/decay factor :
(e) 3-unit growth decay factor :
(f) Initial value : initial value =
(g) Function : f(x) = 25
(
(
(
)1/2
40
15.625
)3/2
40
15.625
40
1/2
40
( 15.625
)
)x/2
40
15.625
= 25
8
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