I'm stuck on these questions for my homework anyone knows if they are linear or nonlinear. and I need to know how to write them as a function.
A. Jordan sells watches from an online business. On average, he sells 75 watches a week, for $50 each. This week, he sold only sold 30, so he held a 40% off sale to stimulate more sales. He sold the watches for $30 each during the sale.
B. An online clothing business, on average, gets 600 sales for $25 jackets every 2 months. Recently, they only made 389 sales because their business rival was holding a fall/holiday sale for the season and had varying prices.
whenever you see phrases like
"each" and "for every"
involving constant amounts, then that indicates a linear function.
For example, in A:
If x is the number of watches sold, and y is the revenue, then
y = 50x
the new discount price is 40% off, or 60% of the normal price so
y = (50 * 0.6)x = 30x
Thanks, I understand a bit better now
To determine whether a problem is linear or nonlinear, we need to understand the relationship between the variables involved.
A linear relationship is one where the variables have a constant rate of change, resulting in a straight line when graphed. A nonlinear relationship, on the other hand, does not have a constant rate of change and does not result in a straight line when graphed.
Let's analyze each problem to see if they are linear or nonlinear:
A. In this problem, the number of watches sold (dependent variable) is affected by the price of the watches. The relationship can be described as follows:
- When the price is $50, Jordan sells 75 watches per week.
- When the price is $30, Jordan sold only 30 watches per week.
Notice that the change in price caused a proportional change in the number of watches sold. This indicates a linear relationship, as the rate of change is constant.
To write this relationship as a function, we can let "x" represent the price of the watches and "y" represent the number of watches sold. The function would be:
y = mx + b
Where "m" represents the slope (rate of change) and "b" represents the y-intercept (the starting point of the line). Using the given information, we can determine the values of "m" and "b" and write the function in slope-intercept form.
B. In this problem, the number of jacket sales (dependent variable) is affected by factors such as rival sales, changing prices, and the passage of time. There is no clear, constant relationship between the variables based on the information given. Therefore, this problem exhibits a nonlinear relationship.
Since the relationship is nonlinear, we cannot write it as a simple linear function like in problem A. Instead, it may require a more complex function, such as an exponential or quadratic function, to accurately model the relationship between the variables.
It's important to note that writing functions solely based on the provided information might not capture the complete picture, but it can give you a starting point in understanding the relationship between the variables. For a more accurate analysis, further information or data may be required.