Two companies modeled their profits for one year. company a used the function p(t)=1.8(1.4)^t to represent its monthly profit, p(t), in hundreds of dollars, after t months, where 0 < t ≤ 12. company b used the data in the table to write a linear model to represent its monthly profits. which statement describes the relationship between the profits, predicted be the models, of the two companies?

Option B is the correct answer.

Step-by-step explanation:

Two companies modeled their profits for one year.

(1) Company A used the function P (t) = to represent its monthly profit in hundreds of dollars after time t.

(2) Company B used the data of the table to write a linear model to represent its monthly income.

Let the linear function is P (t) = mt + c

where m is the slope of the line and c is y - intercept.

As per data we find two points (3.5) and (4.10) lying on the line.

so slope of the line =

and point (3.5) passes through the given line

so,  5 = 5 × 3 + c

      5 = 15 + c

      c = 5 - 15 = - 10

So function will be P (t) = 5t-10

Now at t = 4

Company (A) profit P(4) =   = 6.91

Company (B) profit p (4) = 5 × 4 - 10 = 10

so at t = 4 profits of Company B are more than Company A.

At t = 12

Company A  profit P (12) =    = 102.05

Company B  profit P (12) = ( 5×12 ) - 10 = 66 - 10 = 50

So profit of company A is more at the end of the year.

Option B is the answer.