Math

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

Studdy Solution

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+120.4C = 1.9x + 120.4.
4. Model 2 is given by the formula C=0.03x2+1.8x+120.7C = 0.03x^2 + 1.8x + 120.7.
5. In both models, CC represents the cost xx years after 2010 of what cost 100in1999.<br/>6.Thegraphestimateforthecostin2018is100 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=20182010x = 2018 - 2010

STEP 3

Now, calculate the value of xx.
x=20182010=8x = 2018 - 2010 = 8

STEP 4

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

STEP 5

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

STEP 7

Perform the multiplication.
C=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 = 135.6

STEP 9

Round the cost to the nearest dollar as instructed.
C$136C \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,andthecostcalculatedusingModel1isapproximately135, 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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