Question

a tech company is analyzing the growth of its user base for a new app. the number of users ( u(t) ) it has after ( t ) months is modeled by the exponential function: ( u(t) = 1800(1.09)^t ) interpret the constant rate of change per month for the number of users of the app. show your work here (\bigcirc) the number of users of the app increases by 9% per month (\bigcirc) the number of users of the app doubles every 9 months (\bigcirc) the number of users of the app decreases by 9% per month (\bigcirc) the number of users of the app increases by 9 users every month

Explanation:

Step1: Recall exponential growth form

The standard exponential growth function is $U(t) = U_0(1+r)^t$, where $U_0$ is the initial amount, $r$ is the monthly growth rate, and $t$ is time in months.

Step2: Match given function to standard form

Given $U(t) = 1800(1.09)^t$, we can rewrite it as $U(t) = 1800(1+0.09)^t$.

Step3: Identify the growth rate

Comparing to the standard form, $r = 0.09$, which is equivalent to 9% when converted to a percentage. This means the user base grows by 9% each month.

Answer:

The number of users of the app increases by 9% per month