Question

Carlos purchased a leather sofa four years ago for $1,500.00. Since he purchased it, its value has been decreasing by 30% per
year.
A. Find the missing values for the table shown.
B. Explain how you found each of the missing values in the table.
Carlos purchased it. Then
C Write an expression in the form a(b) that represents the value of the sofa in dollars t years
est your expression for t=0,1,2,3, and 4. Show your work.

Answer 1

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)    $1,500(0.7)^t$: 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

• 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

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 $a(b)^t$ 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:

• $1,500(0.7)^t$

Test it for t = 0, 1, 2, 3, and 4:

• 1,500(0.7)⁰ = 1,500(1) = 1,500   $\checkmark$

• 1,500(0.7)¹ = 1500(0.7) = 1,050  $\checkmark$

• 1,500(0.7)² = 1,500(0.49) = 735  $\checkmark$

• 1,500(0.7)³ = 1500(0.343) = 514.5  $\checkmark$

• 1,500(0.7)⁴ = 1,500(0.2401) = 360.15  $\checkmark$