Solved on Feb 09, 2024

Determine the cost in 2018 of an item that cost $100 in 1999 using a line graph and two models:$ C = 1.9x + 120.4 $and$ C = 0.03x^2 + 1.8x + 120.7 $, where$ C $is the cost$ x$ years after 2010.

STEP 1

Assumptions
1. The base year for the cost calculation is 1999.
2. The year for which we want to calculate the cost is 2018.
3. Model 1 is given by the formula $C = 1.9x + 120.4$ .
4. Model 2 is given by the formula $C = 0.03x^2 + 1.8x + 120.7$ .
5. In both models, $C$ represents the cost $x$ years after 2010 of what cost $100 in 1999.<br />6. The graph estimate for the cost in 2018 is$ 135.

STEP 2

First, we need to calculate the number of years after 2010 that corresponds to the year 2018.
$x = 2018 - 2010$

STEP 3

Now, calculate the value of $x$ .
$x = 2018 - 2010 = 8$

STEP 4

Next, we will use Model 1 to calculate the cost in 2018. We will substitute $x = 8$ into the Model 1 formula.
$C = 1.9x + 120.4$

STEP 5

Substitute $x = 8$ into the Model 1 formula.
$C = 1.9(8) + 120.4$

STEP 6

Calculate the cost using Model 1.
$C = 1.9 \times 8 + 120.4$

STEP 7

Perform the multiplication.
$C = 15.2 + 120.4$

STEP 8

Now, add the values to find the cost in 2018 according to Model 1.
$C = 15.2 + 120.4 = 135.6$

STEP 9

Round the cost to the nearest dollar as instructed.
$C \approx \$136$

STEP 10

Finally, we compare the result from Model 1 with the graph estimate.
The graph estimate for the cost in 2018 is $135, and the cost calculated using Model 1 is approximately$ 136. The model's estimate is very close to the graph estimate, differing by about $1, which indicates that Model 1 describes the estimate from part (a) quite well.

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Determine the cost in 2018 of an item that cost $100 in 1999 using a line graph and two models:$ C = 1.9x + 120.4 $and$ C = 0.03x^2 + 1.8x + 120.7 $, where$ C $is the cost$ x$ years after 2010.

STEP 1

STEP 2

First, we need to calculate the number of years after 2010 that corresponds to the year 2018.
$x = 2018 - 2010$

STEP 3

Now, calculate the value of $x$ .
$x = 2018 - 2010 = 8$

STEP 4

Next, we will use Model 1 to calculate the cost in 2018. We will substitute $x = 8$ into the Model 1 formula.
$C = 1.9x + 120.4$

STEP 5

Substitute $x = 8$ into the Model 1 formula.
$C = 1.9(8) + 120.4$

STEP 6

Calculate the cost using Model 1.
$C = 1.9 \times 8 + 120.4$

STEP 7

Perform the multiplication.
$C = 15.2 + 120.4$

STEP 8

Now, add the values to find the cost in 2018 according to Model 1.
$C = 15.2 + 120.4 = 135.6$

STEP 9

Round the cost to the nearest dollar as instructed.
$C \approx \$136$

STEP 10

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Determine the cost in 2018 of an item that cost 100in1999usingalinegraphandtwomodels:100 in 1999 using a line graph and two models: 100in1999usingalinegraphandtwomodels:C = 1.9x + 120.4and and andC = 0.03x^2 + 1.8x + 120.7,where, where ,whereCisthecost is the cost isthecostx$ years after 2010.

STEP 1

STEP 2

First, we need to calculate the number of years after 2010 that corresponds to the year 2018.x=2018−2010x = 2018 - 2010x=2018−2010

STEP 3

Now, calculate the value of xxx.x=2018−2010=8x = 2018 - 2010 = 8x=2018−2010=8

STEP 4

Next, we will use Model 1 to calculate the cost in 2018. We will substitute x=8x = 8x=8 into the Model 1 formula.C=1.9x+120.4C = 1.9x + 120.4C=1.9x+120.4

STEP 5

Substitute x=8x = 8x=8 into the Model 1 formula.C=1.9(8)+120.4C = 1.9(8) + 120.4C=1.9(8)+120.4

STEP 6

Calculate the cost using Model 1.C=1.9×8+120.4C = 1.9 \times 8 + 120.4C=1.9×8+120.4

STEP 7

Perform the multiplication.C=15.2+120.4C = 15.2 + 120.4C=15.2+120.4

STEP 8

Now, add the values to find the cost in 2018 according to Model 1.C=15.2+120.4=135.6C = 15.2 + 120.4 = 135.6C=15.2+120.4=135.6

STEP 9

Round the cost to the nearest dollar as instructed.C≈$136C \approx \$136C≈$136

STEP 10

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Determine the cost in 2018 of an item that cost $100 in 1999 using a line graph and two models:$ C = 1.9x + 120.4 $and$ C = 0.03x^2 + 1.8x + 120.7 $, where$ C $is the cost$ x$ years after 2010.

First, we need to calculate the number of years after 2010 that corresponds to the year 2018.
$x = 2018 - 2010$

Now, calculate the value of $x$ .
$x = 2018 - 2010 = 8$

Next, we will use Model 1 to calculate the cost in 2018. We will substitute $x = 8$ into the Model 1 formula.
$C = 1.9x + 120.4$

Substitute $x = 8$ into the Model 1 formula.
$C = 1.9(8) + 120.4$

Calculate the cost using Model 1.
$C = 1.9 \times 8 + 120.4$

Perform the multiplication.
$C = 15.2 + 120.4$

Now, add the values to find the cost in 2018 according to Model 1.
$C = 15.2 + 120.4 = 135.6$

Round the cost to the nearest dollar as instructed.
$C \approx \$136$