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.
t | y
1 | 0.98
2 | 0.96
3 | 0.94
4 | 0.92
5 | 0.90
6 | 0.89
(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 130000 dollars. (round to the nearest dollar as needed.)
(b) estimate the cost of a $40 textbook in 4 years.
the textbook will cost about \\(\square\\) dollars. (round to the nearest cent as needed.)

Explanation:

Step1: Find y for t=5, compute house cost

The value of $1 in 5 years is y=0.90. To find the future cost, divide the current cost by this value:
$$\text{House Cost} = \frac{117000}{0.90}$$

Step2: Calculate the house cost

$$\frac{117000}{0.90} = 130000$$

Step3: Find y for t=4, compute textbook cost

The value of $1 in 4 years is y=0.92. To find the future cost, divide the current cost by this value:
$$\text{Textbook Cost} = \frac{40}{0.92}$$

Step4: Calculate the textbook cost

$$\frac{40}{0.92} \approx 43.48$$

Answer:

(a) 130000 dollars
(b) 43.48 dollars