The function gives an app's predicted number of active users, months after the app launched, where . What is the best interpretation of the statement " is approximately equal to " in this context?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 196 | Free SAT Prep | Aniko

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Question 196·Easy·Nonlinear Functions

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The function $g(t) = 12{,}000(1.15)^t$ gives an app's predicted number of active users, $t$ months after the app launched, where $0 < t \le 6$ .

What is the best interpretation of the statement " $g(4)$ is approximately equal to $20{,}988$ " in this context?

For interpretation questions with function notation, first restate what the function gives (for example, total amount vs. change) and what the variables represent. Then plug in the given input (like $t=4$ ) in words—“4 months after launch”—and decide whether the output should be a total, an increase, or a comparison. Finally, scan the choices and eliminate any that (1) talk about change or percentages when the function gives totals, or (2) mention the previous month or other times that are not part of the single function value you are interpreting.

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Focus on what $g(t)$ represents

Read the sentence that defines $g(t)$ . Does $g(t)$ describe a total number of users at time $t$ , or a change in the number of users?

What does plugging in $t=4$ mean?

If $t$ is the number of months after launch, what specific time does $t=4$ refer to in words?

Interpret the approximate value

If $g(4)$ is approximately $20{,}988$ , think: At that specific time, is $20{,}988$ representing a total number of users, or a difference or percentage compared with another month?

Beware of comparisons to the previous month

Some choices mention how this number compares to the previous month. Ask yourself: does $g(4)$ by itself tell you anything about $g(3)$ , or does it just give the value at $t=4$ ?

Desmos Guide

Enter the function

Type g(t) = 12000*(1.15)^t into Desmos. You can use x instead of t if you prefer; just be consistent.

Evaluate the function at 4 months

Either add a table for the function and include the input 4, or type a separate line g(4) (or the equivalent with x). Look at the output value that Desmos shows for this input.

Match the graph/table result to the context

Interpret the numerical output you see for input 4 in words: what time does that input represent, and what quantity (total, increase, or comparison) does the output represent? Choose the answer choice that matches that interpretation.

Step-by-step Explanation

Understand what the function represents

The function is $g(t)=12{,}000(1.15)^t$ . The problem says $g(t)$ gives the app's predicted number of active users, $t$ months after the app launched.

So for any input $t$ , $g(t)$ outputs the total predicted number of users at that time.

Interpret $g(4)$ in words

If $t$ is the number of months after launch, then plugging in $t=4$ means we are looking at the prediction 4 months after the app launched.

So $g(4)$ means: the predicted number of active users 4 months after launch (a total amount at that time, not an amount of increase).

Connect $g(4)$ to the number 20,988

Now we are told that $g(4)$ is approximately equal to $20{,}988$ .

That means when we evaluate $g(4)$ (by plugging $t=4$ into the function), we get a value close to $20{,}988$ . In context, this is the predicted number of users at $t=4$ .

Match this meaning to the answer choice

Putting it all together:

$t=4$ means 4 months after launch.
$g(4)$ is the total predicted number of users at that time.
$g(4)\approx 20{,}988$ means the app is predicted to have about 20,988 active users then.

So the correct interpretation is: 4 months after the app launched, its predicted number of active users is approximately 20,988.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation