186121 (9 complete) A company estimates that its sales will grow continuously at

Question

186121 (9 complete) A company estimates that its sales will grow continuously at a rate given by the function s'(t)-22e 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 first 3 days. b) Find the sales from the 2nd day through the 5th day. (This is the integral from 1 to 5.) a)The accumulated sales for the first 3 days is SO Round to the nearest cent as needed.) b) The sales from the 2nd day through the 5th day is (Round to nearest cent as needed.) Enter your answer in each of the answer boxes

Explanation / Answer

a) We have given S'(t)=22et is the rate at which sales are increasing, in dollars per day,on day t.

The accumulated sales for the first 3 days is integration of (0 to 3) S'(t)dt

integration of (0 to 3) S'(t)dt=integration of (0 to 3) 22et dt

=[22et] from 0 to 3

=[22e^(3)-22e^(0)]

=22[e3-1]

=419.88181231

The accumulated sales for the first 3 days is $419.88

b) The sales from the 2nd day through the 5th day is integration of (1 to 5) S'(t)dt

integration of (1 to 5) S'(t)dt= integration of (1 to 5) 22et dt

=[22et] from 1 to 5

=[22e5-22e1]

=3205.2873

The sales from the 2nd day through the 5th day is $3205.28

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