Question 782·Easy·Math

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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?

In function notation, the number in parentheses is the input, and the function gives an output. When the input measures time, translate it into a time in the story. Define the rule in Desmos and evaluate it to check the output. Don't confuse the total at that time with an increase since an earlier time.

Hints

Hint 1
The number inside a function's parentheses is its input. Here the input measures months since launch, so $g(4)$ points to month 4. What quantity does the problem say $g$ predicts?
Hint 2
A function's output is the result it gives for an input. The problem says this function predicts the number of active users. Is that the number active at a given time or the number gained?

Step-by-step

Read the input and output
Step 1
Identify the time
The $4$ in $g(4)$ is the input, the value put into the function. Since $t$ measures months after launch, $g(4)$ refers to 4 months after launch, not four times the previous month's count.
Step 2
Check the function value
Type $g(t)=12000(1.15)^t$ , then $g(4)$ to put $4$ in for $t$ . Desmos shows $20{,}988.075$ .
Step 3
Put the output into words
An output is the result the function gives. The problem says $g$ predicts the number of active users, not the number gained. Interpret a function value as the quantity the function models at that input. Four months after launch, the app's predicted number of active users is approximately $20{,}988$ . Choice D.

Question 782·Easy·Math

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