Consumer awareness in 1986, the average cost of a new midsize four-door sedan was $9000. in 1991, the average cost was $12,000. determine an exponential model for predicting the cost of a new midsize car. use the model to predict the cost of a comparable new car in the year 2000.

Answer-

And cost of a car in the year 2000 will be $20134.18

Solution-

Let's assume,

x = number of years after 1986

y = average cost of sedan in dollar

The exponential model that will model the scenario will be in the form of,

where a and b are constants

As given that, in 1986 average cost of sedan was $9000 and in 1991 average cost of sedan was $12000

So, the points (0, 9000) and (5, 12000) will satisfy or lie on the exponential curve.

Putting (0, 9000) in the equation,

Now, the equation becomes

Putting (5, 12000) in this equation,

Putting the values,

As we have to calculate the cost of sedan in 2000, so putting x=14(as 2000-1986=14),

Therefore, cost of a car in the year 2000 will be $20134.18

a negative exponent is translated as follows:

so, we have