S'(t)= -147.78e^(-0.2t)
S=7389 units when t=0
find the function that describes the number of daily sales t days after the end of the campaign
Really stuck can someone help me to just find the function so I can head in the right track for the rest of the question
let f(t)= e^kt + C
then f'(t)= k e^kt
so here you are given S', integrate to get S. Don't forget the constant of integration.
To find the function that describes the number of daily sales, we need to integrate the given expression S'(t) = -147.78e^(-0.2t) to obtain S(t).
Let's perform the integration.
∫ S'(t) dt = ∫ -147.78e^(-0.2t) dt
Integrating e^(-0.2t) gives us -(1/0.2)e^(-0.2t) = -5e^(-0.2t).
So, the integral of S'(t) is S(t) = -5e^(-0.2t) + C, where C is the constant of integration.
Now, we have S(t) = -5e^(-0.2t) + C.
To find the value of C, we can use the given information that S = 7389 units when t = 0.
Substitute t = 0 and S = 7389 into the equation:
7389 = -5e^(-0.2(0)) + C
Simplifying this equation, we have:
7389 = -5e^0 + C
7389 = -5 + C
Rearranging the equation to solve for C, we get:
C = 7389 + 5
C = 7394
Therefore, the function that describes the number of daily sales t days after the end of the campaign is:
S(t) = -5e^(-0.2t) + 7394.
Now you can proceed to solve the rest of the question using this function.