Exponential Growth Model User Estimate

A company models the growth of its user base using the exponential function $$N(t) = N_0 e^{kt}$$, where:

• $$N(t)$$ is the number of users after time $$t$$,
• $$N_0$$ is the initial number of users,
• $$k$$ is the growth constant, and
• $$t$$ is the time in months.

Initially, the company has 500 users, and after 3 months, the number of users grows to 750. Using this information, find the estimated number of users after 6 months.