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

To find the function that describes the number of daily sales t days after the end of the campaign, we need to integrate the rate of change of sales (S'(t)) with respect to time.

Given that S'(t) = -147.78e^(-0.2t), we can integrate this expression to find S(t).

∫S'(t) dt = ∫[-147.78e^(-0.2t)] dt

To integrate the expression, we can use the power rule of integration in reverse, where the integral of e^x is e^x divided by the derivative of x.

Using this rule, we can rewrite the integral as:

∫S'(t) dt = -147.78 ∫[e^(-0.2t)] dt

Now, let's integrate e^(-0.2t).

We can do this by letting u = -0.2t, then du = -0.2dt.

The integral becomes:

-147.78 ∫[e^u] du

To integrate e^u, we can simply use the power rule of integration, where the integral of e^x is e^x.

So, the integral becomes:

-147.78 [e^u] + C

Now, let's substitute back the original variable t:

-147.78 [e^(-0.2t)] + C

Since we are looking for the number of daily sales, we can set the constant C as the initial number of sales, S(0) = 7389 units.

So, the function that describes the number of daily sales t days after the end of the campaign is:

S(t) = -147.78 [e^(-0.2t)] + 7389 units