Final answer:
The function that represents the number of followers after weeks for a social media account with a 7% weekly growth rate, starting with 200 followers, is P(t) = 200(1 + 0.07)^t.
Step-by-step explanation:
James' number of followers is increasing at a rate of 7% per week. The function that represents the growth of his followers can be modeled using an exponential growth formula. This is a common scenario in populations or accounts experiencing a consistent percentage growth over time.
The formula for exponential growth is typically written as P(t) = P0(1 + r)^t, where:
P(t) is the number of followers at time t (in weeks)
P0 is the initial amount of followers
r is the growth rate per period (in this case, per week)
t is the number of periods (weeks)
In James' scenario, P0 is 200, and r is 0.07 (since 7% can be written as 0.07 when converted to decimal form). The function that represents his number of followers after t weeks is therefore:
P(t) = 200(1 + 0.07)^t
This function can be used to calculate James' followers at any given point in the future, as long as the growth rate remains constant at 7% per week.