Question 542·Easy·Algebra

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While an aquarium is being refilled, the volume of water in the tank, in liters, is modeled by the function $V(t)=45t+200$ , where $t$ is the number of minutes since pumping began. Which of the following best describes the meaning of $45$ in this model?

In a linear model with time multiplied by a number, that number is the slope: how much the output changes for each unit of time. The separate constant is the starting amount. Read the output and input units to describe the slope as a rate. Don't mistake the number multiplying time for the amount already there.

Hints

Hint 1
In a linear model written as $V(t)=mt+b$ , setting $t=0$ makes $mt=0$ , so $b$ is the starting value. Which part of the given expression stays when $t=0$ ?
Hint 2
A rate compares a change in one quantity with a change in another. The output $V$ and input $t$ use different units; what units would the coefficient multiplying $t$ need to make the equation's terms agree?

Step-by-step

Read the rate from the model
Step 1
Identify the slope
No Desmos needed. The number multiplying time directly gives the rate. In a linear model $V(t)=mt+b$ , the slope $m$ tells you how much the volume changes when time increases by one minute. In $V(t)=45t+200$ , $m=45$ . The separate $200$ is the starting volume, not the rate.
Step 2
Give the rate its meaning and units
The coefficient of time has units of output per input. Here the output is in liters and the input is in minutes, so $45$ means 45 liters per minute. It's positive, so water is being added to the aquarium at that rate. Choice B.

Question 542·Easy·Algebra

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