You have sold 100 I Calculus Tshirts and sales appear to be

You have sold 100 \"I Calculus\" T-shirts and sales appear to be doubling every five days. You estimate the total market for \"I Calculus\" T-shirts to be 5,000. Give a logistic model for your sales.

Use your model to predict, to the nearest day, when you will have sold 800 T-shirts.
( )days

Solution

N(t) = N(0)*e^(kt)

So, 100 = 5000*e^(k*1)

and 200 = 5000*e^(k*5)

Then 2 = e^5k/e^k = e^4k ========> k = 0.1733

So model is N(t) = N(0)*e^(0.1733*t) , t = time in days

b) 800 = 5000*e^(0.1733*t) =====> t = 10.6 days