Question

Let ŷ represent the profit (in thousands of dollars) for a certain company x years after 1970. A statistician calculates a linear model ŷ = 0.66 x + 12 Use the model to estimate the profit in 1978. Your answer should be in dollars, not thousands of dollars.

Answer 1

$17,280

Explanation:

The model for profit (y), in thousands of dollars, as a function of time (x), in years after 1970 is:

`y=0.66x +12`

The corresponding value of x in 1978 is:

`x= 1978-1970\\x=8`

Estimating the profit (in thousands of dollars) in 1978:

`y(8)=0.66*8 +12\\y(8) = 17.28`

Converting it to dollars:

`P = \$1,000*y(8)= \$1,000*17.28\\P= \$17,280`

The estimated profit in 1978 is $17,280.