Remember: if a quantity changes by a fixed amount each time, one type of model is appropriate; if it changes by a fixed percentage (so you keep multiplying by the same factor), a different type of model is appropriate.

The app's users are increasing by 12% each month. Think about whether that means the function’s values go up or down as time increases, and then choose the option whose description matches that behavior.

In Desmos, type the function

(You can use N(t)=2500*(1.12)^t in Desmos.) This represents the number of users after $t$ months.

To see the difference between percent growth and constant-addition growth, also type

where 300 is 12% of 2500. This shows what it would look like if you added the same number of users every month instead of increasing by a percentage.

Look at the graph of $N(t)$: it should curve upward and get steeper as $t$ increases, meaning the number of users is increasing and not following a straight line. Choose the answer choice that describes a function that both increases over time and has a curved (not straight) growth pattern.

We are told:

• The app has 2,500 users to start.
• The number of users increases by 12% each month.

An "increase by 12% each month" means that each month, the new number of users is the previous number of users plus 12% of that previous number.

If a quantity increases by the same percentage each time period, you multiply by the same factor each time.

Here, increasing by 12% means each month you multiply the current number of users by $1+0.12=1.12$.

So after $t$ months, the number of users $N$ can be written in the form

This is a model where the input ($t$ in months) is in the exponent.

Look at the base of the exponent, $1.12$.

• If the base is greater than 1, repeated multiplication by this factor makes the output grow as $t$ increases.
• If the base were between 0 and 1, repeated multiplication would make the output shrink.

Since $1.12>1$, the number of users increases over time.

A function where the variable is in the exponent, like $N(t)=2500\cdot(1.12)^t$, is called an exponential function. Because its base $1.12$ is greater than 1, it is an increasing exponential function.

So the relationship between the number of users and time in months is best modeled by an increasing exponential function, which corresponds to answer choice C) Increasing exponential.