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# Liberty MATH 114 Test 4 Answers Complete Solutions

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A salesperson earns a base income of $200 a week plus 30% commission on the dollar value of each sale. Write a function to represent the amount of his weekly income, I , based on dollar value of sales, x . If his sales for the week totaled $3,000, what is his income for the week?

### Part 1

The amount of the salesperson’s weekly income based on dollar value sales is represented by the function I ( x ) =

Answer

### Part 2

The salesperson will make $ for $3,000 in sales.

The United States Census Bureau uses demographic information to set a poverty threshold that is used to determine how many Americans are living in poverty based on annual income. For an individual on her own, the poverty threshold was $4210 in 1980, and has increased by about $240 per year since then.

### Part 1

Which piece of information in the problem is a rate of change?

The rate of change is .

Answer

### Part 2

What would the rate of change represent in a linear function modeling the poverty threshold?

This would be the in our model.

The United States Census Bureau uses demographic information to set a poverty threshold that is used to determine how many Americans are living in poverty based on annual income. For an individual on her own, the poverty threshold was $4200 in 1980, and has increased by about $210 per year since then.

## STATUS

### Part 1

Write a linear function that describes the poverty threshold in terms of years after 1980. Use x for years since 1980 and T ( x ) to stand for the poverty threshold.

The linear function is T ( x ) =

Answer

### Part 2

Estimate the poverty threshold in 2010.

The poverty threshold was approximately $ in 2010.

### Part 3

In what year will the poverty threshold pass $13,000 per year?

The poverty threshold will pass $13,000 per year in

A contestant on The Biggest Loser starts out weighing 330 pounds and loses weight steadily at the rate of 8 pounds per week.

### Part 1

Write a linear function that describes the contestant’s weight in terms of weeks. Let x stand for number of weeks since the contest began, and let W ( x ) be the contestant’s weight.

A linear function that represents this situation is W ( x ) = x

Answer

### Part 2

Find how long it will take the contestant to reach his goal of 180 pounds. Round to the nearest tenth.

It will take the contestant about weeks to reach his goal weight of 180 pounds.

The cost (in dollars) for a speeding ticket is given by the polynomial 105 + 10 x . In this context, x is the number of miles per hour a motorist travels over the speed limit.

### Part 1

a. Evaluate the polynomial for x = 25. Interpret the answer in the context of this problem.

This means a speeding ticket is $ for speeding mph over the speed limit

Answer

### Part 2

b. Evaluate the polynomial for x = 40. Interpret the answer in the context of this problem.

This means a speeding ticket is $ for speeding mph over the speed limit