2. Poe\'s TV & Repair Co. is now using social networking to expand their reputat

Question

2. Poe's TV & Repair Co. is now using social networking to expand their reputation and reach new potential customers. The company has found that the number N of new potential customers in their 12,000 people community that have heard of their company can be modeled by the equation

N = 12,000(1 - e^-0.0008t)

where t is the number of days elapsed since starting using social networking.

a) How long will it take for 100 new potential customers to have heard of the company?

b) What is the rate of change in time of the number of people who have heard about the company?

Explanation / Answer

a)N = 12,000(1 - e^-0.0008t)

100 = 12000(1-e^(-0.0008t)

t = 10.46 days

b)

N = 12,000(1 - e^-0.0008t)

dN/dt = 12000 (0.0008 e^-0.0008t)

= 9.6 e^-0.0008t

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