Find Formula

Question

The rate of growth of sales (sales per day) for a particular company is predicted to be 45e^0.01t, beginning with sales of 800 items on day t = 0.

Find a formula for the total number of sales in the first t days.

Answer 1

dP/dt = 45e^0.01t

 

with initial condition      P(0) = 800

 

 

Find P(t) by integrating dP/dt.

 

P(t) = 45∫e^0.01tdt

 

P(t) = 45(e^0.01t / 0.01) + C

 

P(t) = 4500e^0.01t + C

 

 

Now solve for C using the initial condition.

 

800 = 45000 + C

 

-3700 = C

 

P(t) = 4500e^0.01t - 3700