Question 638·Easy·Math

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The function $N(t) = 50(1.2)^t$ gives the predicted number of app downloads, in thousands, for a new app, where $t$ is the number of days after the app is released. According to the model, what is the best interpretation of the statement " $N(3)$ is approximately equal to $86.4$ "?

In function notation such as $N(t)$ , the number in parentheses is the input, and the function value is the output. Read the problem’s units to learn what each one measures. You can define the given function in Desmos and evaluate it at the stated input. The key trap is confusing the amount at a time with the increase over an interval.

Hints

Hint 1
The input is the number inside the parentheses. The problem says $t$ counts days after release, so what time does the $3$ in $N(3)$ represent?
Hint 2
The output is the number the function predicts, measured here in thousands of downloads. An increase over the first $3$ days would require subtracting the release-day output. Is that subtraction part of $N(3)$ ?

Step-by-step

Read the input and output
Step 1
Identify the time
The input is the number inside the parentheses. Since $t$ counts days after release, the $3$ in $N(3)$ means $3$ days after release, not $3$ thousand downloads.
Step 2
Identify what the output measures
The output $N(t)$ is the predicted number of downloads at time $t$ , not the increase since release. The problem measures that output in thousands, so $86.4$ means $86.4$ thousand downloads. An increase over the first $3$ days would be $N(3)-N(0)$ .
Step 3
Evaluate and put the units together
Type $N(t)=50(1.2)^t$ , then $N(3)$ on the next line. Desmos shows $86.4$ , confirming the stated value. Pair that output with its time and unit: $3$ days after release, the predicted number of downloads was approximately $86.4$ thousand. Choice C.

Question 638·Easy·Math

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