Question

3 feeding 54C 3. What is the constant of proportionality? What does it tell us about the situation? day 4. If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning. 5. Use d for number of days and f for amount of food in grams that a shrimp eats to write two equations that represent the relationship between d and f. 6. If a tank has 10 shrimp in it, how much food is added to the tank each day? 7. If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.

Answer 1

3) 0.6 grams per day

4) 1.67 grams per day

5) f = kd

k = f/d

Step-by-step explanation:

3) y = kx

where k = constant of proportionality

from the table, let x = number of days

y = food in grams

when x = 1, y = 0.6

we find k:

0.6 = k(1)

0.6 = k

Hence, the constant of proportionality is 0.6

It means the rate at which the shrimp is fed is 0.6grams per day

4) if columns are switched, the number of days = y

food in grams = x

let's use the same values but it will be interchanged:

when x = 0.6, y = 1

y = kx

1 = k(0.6)

1 = 0.6k

k = 1/0.6

k = 1.67 or 5/3

The rate at which the shrimp is fed is 1.67 grams per day

Here the rate is higher than the previous result. This is because the y value is greater then the x value.

5) if f = amount of food in grams

d = number of days

Since the relationship between the amount of food and number of days is proportional (it has beeen established previously), we would use the proportional equation:

y = f = amount of food in grams

x = d = number of days

f = kd (one equation)

it can also be written as:

f = kd

k = f/d (2nd equation)