Question

if money loses value, then as time passes, it takes more dollars to buy the same item. use the table to answer the questions. let t be years and y be the value of $1 in t years.
\begin{tabular}{|c|c|} hline t & y \\ hline 1 & 0.98 \\ hline 2 & 0.96 \\ hline 3 & 0.94 \\ hline 4 & 0.92 \\ hline 5 & 0.90 \\ hline 6 & 0.89 \\ hline end{tabular}
(a) suppose a house costs $117,000 today. estimate the cost of the same house in 5 years.
(b) estimate the cost of a $40 textbook in 4 years.
(a) suppose a house costs $117,000 today. estimate the cost of the same house in 5 years.
the house will cost about \boxed{} dollars. (round to the nearest dollar as needed.)

Explanation:

Step1: Find y for t=5 (house)

From table, $y=0.90$ when $t=5$.

Step2: Calculate inverse of y (inflation factor)

$\frac{1}{0.90} \approx 1.1111$

Step3: Compute house cost in 5 years

$117000 \times \frac{1}{0.90} = 117000 \times 1.1111$

Step4: Find y for t=4 (textbook)

From table, $y=0.92$ when $t=4$.

Step5: Calculate inverse of y (inflation factor)

$\frac{1}{0.92} \approx 1.0870$

Step6: Compute textbook cost in 4 years

$40 \times \frac{1}{0.92} = 40 \times 1.0870$

Answer:

(a) The house will cost about 130000 dollars.
(b) The textbook will cost about 43 dollars.