Sean intends to collect $500 in individual donations for a charity. His company will contribute $2 for every donation collected. Write and graph an equation that gives the average amounta (including the company contribution) that the charity will receive per individual donation as a function of the number d of donations.
If there are d donations totalling m dollars, then the charity receives
t = 2d+m
that means the average is
a = (2d+m)/d = 2+m/d
If the total of donations is exactly 500 as desired, then
a(d) = 2 + 500/d
To find the average amount the charity will receive per individual donation, we need to consider both the individual donations and the company contributions.
Let's denote the average amount received per individual donation as A(a), where a is the number of donations collected.
The amount collected from individual donations alone would be 500 (since Sean intends to collect $500).
The amount collected from the company would be 2 times the number of donations, as the company contributes $2 per donation. Therefore, the amount collected from the company would be 2a.
The total amount received by the charity would be the sum of the individual donations and the company contributions:
Total amount received = Amount from individual donations + Amount from company contributions
= 500 + (2a)
The average amount per individual donation is given by dividing the total amount received by the number of donations:
A(a) = (500 + 2a) / a
To graph this equation, we can plot the average amount received per individual donation on the y-axis, and the number of donations on the x-axis. The graph will have a line with a positive slope, as the average amount per donation increases as the number of donations increases.
To find the average amount that the charity will receive per individual donation, we need to consider the total amount collected and the total number of donations.
Let's break down the contributions:
- Sean will collect $500 in individual donations.
- His company will contribute $2 for every donation.
Let's assume the total number of donations is represented by 'd'.
The total amount collected will be the sum of individual donations and the company's contributions. The amount collected from individual donations will be $500, and the company will contribute $2 for every donation. Therefore, the total collected amount can be expressed as:
Total Amount = $500 + ($2 * d)
To find the average amount per individual donation, we need to divide the total amount collected by the total number of donations:
Average Amount = Total Amount / Number of Donations
Average Amount = ($500 + ($2 * d)) / d
Now, let's graph this equation to visualize the relationship between the average amount and the number of donations.
The x-axis will represent the number of donations (d), and the y-axis will represent the average amount received per donation.
Note: The graph will be a linear graph with a positive slope since the average amount will increase as the number of donations increases.
Please keep in mind that the graph might not be accurate for specific numerical values without knowing the exact range of 'd' and the constraints on the equation.