A company estimates that its sales will grow continuously at a rate given by the function S'Ilt): 11.91 where S'(t] is the rate at which sales are increasing; in dollars per day, on day t. a) Find the accumulated sales for the rst 9 days. b) Find the sales from the 2nd day through the 5th day. (This is the integral from t to 5.) E a) The accumulated sales for the first 9 days is 53D. (Round to the nearest cent as needed.) Assume the annual rate of change in the national debt ofa country (in billions of dollars per year) can be modeled by the function D'(t) = 848.93 + 823.661 150.0312 +13_12t3 where t is the number of years since 1995. By how much did the debt increase between 1996 and 2000'? The debt increased by $ billion. (Round to two decimal p aces as needed.) A company is producing a new product. Due to the nature of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 2+ 0.2 - , where T(x) is the time, in hours, required to produce the xth unit. Find the total time required for a new worker to produce units 1 through 5; units 20 through 25. The worker requires | hours to produce units 1 through 5. (Round to two decimal places as needed.)Suppose that in a memory experiment the rate of memorizing is given by M'): 0.006t2 + 0.21 where Mn) is the memory rate, in words per minute. Hon.r many words are memorized in the first 10 min (from t2 O to t: 10)? In the first 10 minutes words are memorized. Suppose that in a memory experiment the rate of memorizing is given by M'(t) = - 0.006t + 0.2t, where M'(t) is the memory rate, in words per minute. How many words are memorized during minutes 20 - 25? - . . words are memorized during minutes 20 to 25. (Round to the nearest number of words as needed.)Let a represent acceleration and v represent velocity. Find v(t). a(t) = 8t, v(0) = 15 V(t) =Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and a(t) represents the acceleration function. a(t) = - 18t + 2, with v(0) = 6 and s(0) = 8 . . . s(t) =A particle is released as part of an experiment. Its Speed t seconds after release lS given by v(t) : 0.3t2 + 2t: where v(t) is in meters per second a) How far does the particle travel during the first 3 sec? b] How far does it travel during the second 3 sec\"? a) The particle travels meters in the first 3 sec (Round to two decima places as needed.)