Question 110·Medium·Linear Functions
The function gives the predicted number of fish remaining in a lake months after a conservation project begins, where .
Based on this model, what is the predicted number of fish remaining after 18 months?
For linear function word problems, first identify what the input variable represents and plug in the given value directly into the function. Then simplify carefully using order of operations: do the multiplication () first, then add or subtract from the initial value. As a quick check, make sure your final answer is reasonable in context (here, the number of fish after some time should be less than the starting 12,500 and positive).
Hints
Focus on what the function inputs and outputs mean
In the function , what does represent? To find the number of fish after 18 months, what value should you plug in for ?
Write the expression you need to evaluate
Substitute into the function. You should get an expression like . What should you calculate first in that expression?
Do the arithmetic step by step
Find (it might help to think of and then multiply by 10). Then subtract that product from 12,500 to get the predicted number of fish.
Desmos Guide
Evaluate the expression in Desmos
In a Desmos expression line, type 12500-350*18 and look at the numerical result; that value is the predicted number of fish remaining after 18 months.
Step-by-step Explanation
Identify the correct substitution
The function gives the number of fish months after the project begins.
For 18 months after the project begins, substitute into the function, so you want to find .
Compute the total decrease after 18 months
First, calculate how many fish are removed in 18 months at a rate of 350 fish per month:
So, a total of 6,300 fish are removed over 18 months.
Subtract from the initial number of fish
Now subtract this total decrease from the initial 12,500 fish:
So, the predicted number of fish remaining after 18 months is 6,200, which corresponds to answer choice B.