Answer:
A) Table:
Value of the sofa in dollars:
Year Value
0 $1,500
1 $1,050
2 $735
3 $514.50
4 $360.15
B) Multiply successively by 0.70
C) [tex]1,500(0.7)^t[/tex]: see the tests below
Explanation:
A) Find the missing values for the table shown
Although the table was not provided with the question, you can create a complete table from the supplied information.
Table: value of the sofa
Year Value
0 $1,500
1 A
2 B
3 C
4 D
Then, determine the missing values, i.e. A, B, C, and D
Notice that 30% is 0.30 and a reduction in the value is determined by mutiplying the starting value by 1 - 0.3 = 0.7.
- A = $1,500 × 0.7 = $1,050.00
- B = $1,050 × 0.7 = $735.00
- D = $514.50 × 0.7 = $360.15
Thus, once completed the table would be:
Year Value
0 $1,500
1 $1,050
2 $735
3 $514.50
4 $360.15
B. Explain how you found each of the missing values in the table.
I multiplied successively by 0.70 which is the constant decaying rate of the function.
C. Write an expression in the form [tex]a(b)^t[/tex] that represents the value of the sofa in dollars t years after Carlos purchased it. Then test your expression for t = 0, 1, 2, 3, and 4.
- a is the purchasing value of the sofa or the value when t = 0: 1,500
- b is the decaying rate: 1 - 30% = 1 - 0.3 = 0.7
Thus, the expression is:
Test it for t = 0, 1, 2, 3, and 4:
- 1,500(0.7)⁰ = 1,500(1) = 1,500 [tex]\checkmark[/tex]
- 1,500(0.7)¹ = 1500(0.7) = 1,050 [tex]\checkmark[/tex]
- 1,500(0.7)² = 1,500(0.49) = 735 [tex]\checkmark[/tex]
- 1,500(0.7)³ = 1500(0.343) = 514.5 [tex]\checkmark[/tex]
- 1,500(0.7)⁴ = 1,500(0.2401) = 360.15 [tex]\checkmark[/tex]
