-3/5, 6/5, -12/5 What is the next term of the geometric sequence ?
1 answer:
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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) : see the tests below
Explanation:
<em>A) Find the missing values for the table shown</em>
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
- C = $735 × 0.7 = $514.50
- 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
<em>B. Explain how you found each of the missing values in the table.</em>
I multiplied successively by 0.70 which is the constant decaying rate of the function.
<em>C. Write an expression in the form </em><em> 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.</em>
- 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
- 1,500(0.7)¹ = 1500(0.7) = 1,050
- 1,500(0.7)² = 1,500(0.49) = 735
- 1,500(0.7)³ = 1500(0.343) = 514.5
- 1,500(0.7)⁴ = 1,500(0.2401) = 360.15