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\(\pi\)
e
\(\frac{a}{b}\)
!
←
→
(
)
\(\sqrt{\,}\)
\(a^{b}\)
7
8
9
\(\div\)
log
ln
4
5
6
\(\times\)
cos
cos⁻¹
1
2
3
-
sin
sin⁻¹
0
.
=
+
tan
tan⁻¹
You buy a car for \(\dollar\)10,000. It depreciates at a rate of 20\(\pourcent\) per year. Depreciation means that each year, the value decreases by 20\(\pourcent\) of the current value, so the remaining value is 80\(\pourcent\) of the previous year's value. Thus, the value multiplies by 0.8 each year.
Let \(u_n\) be the value of the car after \(n\) years. What are the first three terms of the sequence \((u_n)\)?
\(u_1 =\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
dollars
\(u_2 =\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
dollars
\(u_3 =\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
dollars
What is its recursive rule?
\(u_{n+1}=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
What is its explicit rule?
\(u_{n}=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
How many dollars will the car be worth after 10 years? (Round to two decimal places if necessary.)
\(u_{10}=\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
dollars
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