Acompany determines that its marginal revenue per day is given by r' ( t ) , where r ( t ) is the total accumulated revenue, in dollars, on the tth day. the company's marginal cost per day is given by c' ( t ) , where c ( t ) is the total accumulated cost, in dollars, on the tth day. r' ( t ) = 80 e t, r ( 0 ) = 0; c' ( t ) = 80 - 0.8t, c ( 0 ) = 0 find the total profit p ( t ) from t = 0 to t = 10 ( the first 10 days ) . p ( t ) = r ( t ) - c ( t ) = [r' ( t ) - c' ( t ) ] dt the total profit is $ . ( round to the nearest cent as needed. ) find the average daily profit for the first 10 days. the average daily profit is $ . ( round to the nearest cent as needed. )

Step-by-step explanation:

Total profit function is equal to Total revenue function minus Total Cost function.

To get both Revenue function and Cost function, integrate the Marginal functions as follows:

R(t) = 108.7312t^2

Where 80et = 217.4624t

(e =2.71828)

C(t) = 80t - 0.4t^2

P(t) = R(t) - C(t) = 109.1312t^2 - 80t

When t=0, P=0

When t=1, P=29.1312

When t=2, P=276.5248

When t=3, P=742.1808

And so on ...

Summing the daily profits, total profit for the 10 days is 37,615.512 dollars which equals 3,761551.2 cents

(B)

Average daily profit for the first 10 days (in dollars) is 37,615.512÷10 = 3,761.5512 dollars

= 376,155.12 cents

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.

you can't solve x because it is 2 linear equation and you only have one equation