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Math 112 Spring 2024 Midterm 1 Practice Exam Questions

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Math 112 Spring 2024 Midterm 1 Practice Exam Questions

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Questions and Answers

What is the maximum profit according to the given information?

Between $850,000 and $900,000

Between $800,000 and $850,000

More than $900,000 (correct)

Between $750,000 and $800,000

For the linear function graphed below, what is the correct equation?

$y=-x+\frac{1}{2}$

$y=x+1$

$y=2x+1$ (correct)

$y=\frac{1}{x+1}$

Which equation correctly models the depreciation of Samantha's car after t years from the initial purchase?

$D(t)=-3500t$

$D(t)=-3500t+45,000$

$D(t)=-3500t+41,500$ (correct)

$D(t)=-3500t+38,000$

What does the slope of the depreciation function ($-3,500$) indicate in practical terms?

The car decreases in value by $3,500 each year. Signup and view all the answers

What is the initial purchase price of Samantha's car based on the depreciation function?

$$79,500$$ Signup and view all the answers

If Samantha wanted to calculate the car's value after 3 years using the depreciation function, what amount should she expect?

$$34,500$$ Signup and view all the answers

What is the slope of the car's depreciation model?

$-3,500 Signup and view all the answers

Based on the given information, what is the initial purchase price of Samantha's car?

$79,500 Signup and view all the answers

What would be the total cost of the ticket for traveling 25 miles?

$33.00 Signup and view all the answers

If the function definition for f(x) is rearranged to be single-piece, how would it look?

$x + 2$ Signup and view all the answers

What is the expression for the total cost of a subway ticket, C(x), if x represents the number of miles traveled?

$1.30x$ if $x leq 20$, $1.15(x-20)$ if $x > 20$ Signup and view all the answers

Bonus Question: What is the maximum number of miles MJ can travel on the subway with $24?

Between 15 and 17 miles Signup and view all the answers

What does the function y = x - 4 represent in the given context?

The cost of producing each DVD player Signup and view all the answers

How are the x-intercepts related to profit in the context of the DVD player manufacturer's function?

They indicate the number of DVD players needed to break even Signup and view all the answers

What does the value 258 in the profit function represent?

The rate of change of profit Signup and view all the answers

What is the significance of the open interval (150, 6450) in relation to the profit function?

It represents a range of increasing profits Signup and view all the answers

Why is it important for a manufacturer to know the maximum profit according to the model?

To assess potential profits and make business decisions Signup and view all the answers

If a different linear function were to represent revenue instead of cost, how would this impact profit calculations?

It would not affect profits directly as revenue and cost are separate Signup and view all the answers