Question

A company estimates that its sales will grow continuously at a rate given by the function S'(t) = 10 et 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.) 1. a) The accumulated sales for the first 3 days is $ (Round to the nearest cent as needed.) b) The sales from the 2nd day through the 5th day is $ (Round to the nearest cent as needed.) .

Answer 1

we have

$S'(t)=10e^t$

a)

the sales of first 3 days,

$S(t)=\int_{0}^{3}10e^tdt$

$S(t)=[10e^t]_{0}^{3}$

$S(t)=10e^3-10e^0$

S(t) = 103-10

$S(t)=190.86$

b)

the sales of 2nd through 5th day,

$S(t)=\int_{1}^{5}10e^tdt$

$S(t)=[10e^t]_{1}^{5}$

$S(t)=10e^5-10e^1$

$S(t)=10e^5-10e$

$S(t)=1456.95$