Question

QUESTION 10

From 1980 to 2000, the average cost of a new car C (in dollars) can be approximated by the model C = 45.5t^2 +6100 where t
is the number of years since 1980. During which year was the average cost of a new car $ 11,600 ?

Answer 1

To find the year during which the average cost of a new car was $11,600, we can set up the equation and solve for the value of t.

The given model is:

`\sf C = 45.5t^2 + 6100 \\`

We want to find the value of t when C is $11,600. So we can substitute C = $11,600 into the equation:

`\sf 11,600 = 45.5t^2 + 6100 \\`

Now, let's solve this equation for t.

Subtracting 6100 from both sides:

`\sf 11,600 - 6100 = 45.5t^2 \\`

Simplifying:

`\sf 5500 = 45.5t^2 \\`

Dividing both sides by 45.5:

`\sf (5500)/(45.5) = t^2 \\`

Calculating:

`\sf 120.88 \approx t^2 \\`

To find the value of t, we take the square root of both sides:

`\sf t \approx √(120.88) \\`

Calculating:

`\sf t \approx 11.00 \\`

Therefore, the average cost of a new car was $11,600 around the year 1991 (since 1980 + 11 years = 1991).

Thus, the average cost of a new car was $11,600 in the year 1991.