Question

The number of users on a website has grown exponentially. After 1 month, there were 45 users, and after 3 months, there were 405 users. Which function models the number of users x months after the website was launched?

a) f(x)=45×3^x
b) f(x)=45×9^x
c) f(x)=45×2^x
d) f(x)=45+3x

Answer 1

The function that models the number of users x months after the website was launched is option b) f(x)=45×9^x.

Step-by-step explanation:

The function that models the number of users x months after the website was launched is option b) f(x)=45×9^x.

To determine the correct function, we need to consider the growth rate of the number of users. Since the number of users has grown exponentially, the function must have an exponential form. We can find the base of the exponential function by using the given information. After 1 month, there were 45 users, and after 3 months, there were 405 users. This means that the number of users tripled in 2 months (from 45 to 405).

Using the exponential growth formula, where M is the final amount, b is the base, and n is the number of time periods, we can set up two equations to solve for b and n:

Equation 1: 45 × b^n = 405

Equation 2: 45 × b^(n-2) = 45 (since the number of users tripled in 2 months)

Solving these equations, we find that b = 9 and n = 2. Therefore, the function that models the number of users is f(x)=45×9^x.