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Determine whether the data described in the tables is best modeled by a linear function or an exponential function.

Determine whether the data described in the tables is best modeled by a linear function-example-1
Determine whether the data described in the tables is best modeled by a linear function-example-1
Determine whether the data described in the tables is best modeled by a linear function-example-2

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Answer:

Electric car = Exponential function (decreasing cost)

Gasoline car = Exponential function (increasing cost)

Explanation:

The given data the Electric car, we have;

Time (years)
{} Cost (thousands of dollars)

0
{} 35

5
{} 27

10
{} 21

15
{} 16

20
{} 12.5

The difference between successive term is such that each term decreases by approximately the same percentage given as follows

1st and 2nd term (35 - 27)/35 × 100 ≈ 22.8571% decrease

2nd and 3rd term (27 - 21)/27 × 100 ≈ 22.222% decrease

3rd and 4th term (21 - 16)/21 × 100 ≈ 23.81% decrease

4th and 5th term (16 - 12.5)/16 × 100 ≈ 21.875% decrease

Therefore. the electric car is best approximated by exponential function

The given data the Gasoline car, we have;

Time (years)
{} Cost (thousands of dollars)

0
{} 35

5
{} 40.2

10
{} 46.3

15
{} 53.2

20
{} 61.2

The difference between successive term is such that each term increases by approximately the same percentage given as follows

1st and 2nd term (40.2 - 35)/35 × 100 ≈ 14.857% decrease

2nd and 3rd term (46.3 - 40.2)/40.2 × 100 ≈ 15.174% decrease

3rd and 4th term (53.2 - 46.3)/46.3× 100 ≈ 14.9% decrease

4th and 5th term (61.2 - 53.2)/53.2× 100 ≈ 15.03% decrease

Therefore. the Gasoline car is best approximated by exponential function

User JBJ
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