A startup's customer base grows at a rate of dN/dt = 100e^(0.1t) users per month. If they start with 1000 users at t=0, how many users will they have at time t?

A startup's customer base grows at a rate of dN/dt = 100e^(0.1t) users per month. If they start with 1000 users at t=0, how many users will they have at time t?

• A. 1000e^(0.1t)
• B. 1000e^(0.1t) + 1000
• C. 1000e^(0.1t) - 1000
• D. 100e^(0.1t) + 900

Answer: A) 1000e^(0.1t)

Explanation: N(t) = ∫ 100e^(0.1t) dt = 1000e^(0.1t) + C. N(0) = 1000 => 1000(1) + C = 1000 => C = 0.