Question 547·Medium·Algebra

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The function $p(n)=12{,}500-350n$ gives the predicted number of fish $p(n)$ remaining in a lake $n$ months after a conservation project begins, where $0 \le n \le 30$ .

Based on this model, what is the predicted number of fish remaining after 18 months?

An already-written linear function gives an output for each allowed input. If the question asks what remains after a certain time, that time is the input; define the rule in Desmos and evaluate it there. The amount lost over that time is not the same as the amount remaining.

Hints

Hint 1
The number inside function notation, such as $p(n)$ , is the input. The model measures its input in months. Which number belongs inside $p(\cdot)$ for the requested time?
Hint 2
The negative term in a linear model represents a decrease. The monthly decrease repeats, but the starting count is used only once. What expression subtracts the decrease over the requested months?

Step-by-step

Evaluate the fish-count function
Step 1
Turn the time into a function input
The model calls $n$ the number of months, so 18 months is the input, and the fish remaining are the output. In function notation, $p(18)$ means replace $n$ with $18$ : $p(18)=12{,}500-350(18)$ . The $350$ is multiplied by the months because it is the monthly decrease; $12{,}500$ is the starting count, used once.
Step 2
Read the predicted number remaining
Type $p(n)=12{,}500-350n$ in Desmos, then type $p(18)$ on the next line. Desmos shows $6{,}200$ . That output is the fish still in the lake: after $18$ months, the model predicts $6{,}200$ fish remain. Choice B.

Question 547·Medium·Algebra

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