Questions: The line graph shows the cost of inflation in some country. What cost 100 in 1999 would cost the amount shown by the graph in subsequent years. Below are two mathematical models for the data shown in the graph. In each formula, C represents the cost x years after 2010 of what cost 100 in 1999. Answer parts (a) through (c). Model 1 C=1.9x+120.5 Model 2 C=0.02x^2+1.8x+120.6 Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) A. The formula appears to overestimate the cost by 1, when compared to the graph. Thus, the formula describes well the estimate from part (a). B. The formula appears to overestimate the cost by , when compared to the graph. Thus, the formula does not describe well the estimate from part (a). C. The formula appears to underestimate the cost by when compared to the graph. Thus, the formula does not describe well the estimate from part (a). D. The formula appears to underestimate the cost by , when compared to the graph. Thus, the formula describes well the estimate from part (a). c. Use model 2 to determine the cost in 2018 . How well does this describe your estimate from part (a)? The cost in 2018 was approximately (Round to the nearest dollar as needed.)

The line graph shows the cost of inflation in some country. What cost 100 in 1999 would cost the amount shown by the graph in subsequent years. Below are two mathematical models for the data shown in the graph. In each formula, C represents the cost x years after 2010 of what cost 100 in 1999. Answer parts (a) through (c). Model 1 C=1.9x+120.5 Model 2 C=0.02x^2+1.8x+120.6 Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) A. The formula appears to overestimate the cost by 1, when compared to the graph. Thus, the formula describes well the estimate from part (a). B. The formula appears to overestimate the cost by , when compared to the graph. Thus, the formula does not describe well the estimate from part (a). C. The formula appears to underestimate the cost by when compared to the graph. Thus, the formula does not describe well the estimate from part (a). D. The formula appears to underestimate the cost by , when compared to the graph. Thus, the formula describes well the estimate from part (a). c. Use model 2 to determine the cost in 2018 . How well does this describe your estimate from part (a)? The cost in 2018 was approximately (Round to the nearest dollar as needed.)
Transcript text: The line graph shows the cost of inflation in some country. What cost $\$ 100$ in 1999 would cost the amount shown by the graph in subsequent years. Below are two mathematical models for the data shown in the graph. In each formula, C represents the cost $x$ years after 2010 of what cost $\$ 100$ in 1999. Answer parts (a) through (c). Model $1 \quad \mathrm{C}=1.9 \mathrm{x}+120.5$ Model $2 \mathrm{C}=0.02 \mathrm{x}^{2}+1.8 \mathrm{x}+120.6$ Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) A. The formula appears to overestimate the cost by $\$ 1$, when compared to the graph. Thus, the formula describes well the estimate from part (a). B. The formula appears to overestimate the cost by $\$$, when compared to the graph. Thus, the formula does not describe well the estimate from part (a). C. The formula appears to underestimate the cost by \$ when compared to the graph. Thus, the formula does not describe well the estimate from part (a). D. The formula appears to underestimate the cost by $\$$, wheili compared to the graph. Thus, the formula describes well the estimate from part (a). c. Use model 2 to determine the cost in 2018 . How well does this describe your estimate from part (a)? The cost in 2018 was approximately \$ $\square$ (Round to the nearest dollar as needed.)
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Solution

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Solution Steps

Step 1: Calculate the cost using Model 1 for 2018.

x = 2018 - 2010 = 8 C = 1.9 * 8 + 120.5 C = 15.2 + 120.5 C = 135.7 Rounding to the nearest dollar, the cost is $136.

From the graph, the cost in 2018 appears to be $135.

The difference between the model and the graph is 136 - 135 = $1. Since the model predicts a higher value than the graph, it overestimates.

Step 2: Choose the correct option for part (b).

Since Model 1 overestimates the cost by $1, the answer is A.

Step 3: Calculate the cost using Model 2 for 2018.

x = 2018 - 2010 = 8 C = 0.02 * 8^2 + 1.8 * 8 + 120.6 C = 0.02 * 64 + 14.4 + 120.6 C = 1.28 + 14.4 + 120.6 C = 136.28

Rounding to the nearest dollar gives $136.

The difference between the Model 2 estimate and the graphical estimate is $1. Since the model gives a higher value, it overestimates.

Final Answer

a. $136 b. A. The formula appears to overestimate the cost by $1, when compared to the graph. Thus, the formula describes well the estimate from part (a). c. $136

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