Consider the scenario: A job raking leaves pays $10 to get started, then $15 for every hour of work. Decide which type of function best represents how much money the leaf-raker make at a worksite. (1 point)

Question

• a positive exponential function.
• a negative quadratic function
• a negative linear function
• a positive linear function

Answer 1

The scenario describes a job that pays a fixed starting amount and then an hourly wage. The payment structure can be expressed as follows:

• The initial payment is $10.
• For each hour worked, the raker earns an additional $15.

The total money earned after working \( h \) hours can be represented by the equation:

\[ \text{Total Earnings} = 10 + 15h \]

This is a linear equation with a positive slope, indicating that as the hours worked (\( h \)) increase, the total earnings also increase proportionally.

Therefore, the type of function that best represents how much money the leaf-raker makes at a worksite is:

• a positive linear function.

Answer 2

Quavarius sets up an investment account that guarantees a 5% interest compounded monthly. He deposits $100 into his account each month. Which type of function best models the amount of money Quavarius has in his account? (1 point)
• a positive linear function
• a negative quadratic function
• a positive exponential function
• a negative linear function

Answer 3

In this scenario, Quavarius is making monthly deposits into an investment account that earns interest compounded monthly. The situation involves two key components:

1. Monthly Deposits: Quavarius is depositing a fixed amount ($100) each month, which by itself would suggest a linear accumulation of deposits.

2. Compound Interest: The interest is compounded monthly at a rate of 5%, which means the amount of money in the account will grow exponentially over time due to that compounding effect.

The total amount in the account over time is influenced both by the linear growth from his monthly deposits and the additional exponential growth from the interest being compounded.

Since the dominant feature of the account's growth will be the compounding interest effect, the best model for the total amount of money Quavarius has in his account is a positive exponential function.

Therefore, the correct answer is:

• a positive exponential function.

Answer 4

Which scenario would create a graph with a positive slope? (1 point)
• the amount of money that someone makes at a job over the course of a week
• the trajectory of an airplane coming in for a landing
• the elevation of a person going down a waterslide
• the speed of a person sitting on a park bench over time

Answer 5

To determine which scenario would create a graph with a positive slope, let's examine each option:

1. The amount of money that someone makes at a job over the course of a week: This scenario generally involves a steady or increasing amount of money earned over time (assuming regular hours and pay), resulting in a positive slope.

2. The trajectory of an airplane coming in for a landing: This scenario typically has a negative slope as the airplane descends toward the runway.

3. The elevation of a person going down a waterslide: This scenario also typically has a negative slope, as the person's elevation decreases as they go down the slide.

4. The speed of a person sitting on a park bench over time: In this case, the speed remains constant at zero, resulting in a horizontal line (slope of zero).

Given this analysis, the scenario that would create a graph with a positive slope is:

• the amount of money that someone makes at a job over the course of a week.