Question

Calculus" T-shirts and sales appear to be doubling every five days. You estimate the total market for Calculus" Tshirts to be 4,000. Give a logistic model for your sales You have sold 100 " 1 N(t) - Use your model to predict, to the nearest day, when you will have sold 800 T-shirts days

Answer 1

Sales till now = 100

Model will become, y = A*b^t

where A = 100 and t is the number of days it will take tshirt to double.

Thus, 200 = 100 * b⁵ (as tshirt double every 5 days)

2 = b⁵

b = 2^1/5

Thus the function become y = 100 * 2^(t/5)

When 800 tshirts are sold, 800 = 100 * 2^(t/5)

8 = 2^(t/5)

Taking log on both sides,

log 8 = (t/5) * log 2

3 log2 = (t/5) * log2 (log 8 = log 2³)

t = 15

Thus the sales of tshirt will reach 800 after 15 days.