The amount of waste a company produces, W, in metric tons per week, is approximated by W=3.75e-0.008t, where t is in weeks since January 1, 2016. Waste removal for the company costs $105/ton. How much does the company pay for waste removal during the year 2016?

$16749.6 the company pay for waste removal during the year 2016.

Step-by-step explanation:

We know that the amount of waste a company produces, , is given by

where

is in weeks since January 1, 2016.

We want to find the total waste during the year 2016. Therefore, we compute the definite integral

We have a function that describes a rate (). So the definite integral gave us the net change in the amount of waste between January 1, 2016 and December 31, 2016.

The limit of integration 52 is because there are 52 weeks in a year.

The waste removal for the company costs $105/ton. Therefore, the company paid

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves