Algebra Equations Worksheets With Answer Keys Page 16
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20Chapter 5
16
8. Price inflation in the United States is typically about 3% per year. Assuming an annual
inflation rate of 3%, do the following:
(a) Create a model that gives the future price of a candy bar that costs
$0.75 today.
+1 exponential function
( )
(
)
t
p t =
0.75 1.03
+1 initial value is 0.75
+1 growth factor is 1.03
(b) Determine when the price of the candy bar is expected to reach
$1.50.
(
)
(
)
t
t
=
=
+1
1.50 0.75 1.03
1.50 0.75 1.03
+1 Correctly log both sides
=
t
2 1.03
t =
+1
23.450 years
=
ln 2
t
ln1.03
ln 2
=
t
ln1.03
≈
t
23.450 years from now
(c) When the price reaches $1.50, at what instantaneous rate (in
( )
(
)(
)
t
p t ′ =
+1
0.75ln 1.03 1.03
dollars per year) will the price of the candy bar be changing?
+1 0.044
+1 dollars per year
( )
(
) (
)
t
′
=
p t
0.75ln 1.03 1.03
(
)
′
≈
p
23.450
0.044 dollars per year
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