A cat is brought in to the shelter weighing 5.75 pounds. The vet says the cat needs a special diet so that it will gain a quarter of a pound a week until it is 11 pounds.

Question

a. How much will it take before the cat weighs 8 pounds?

b. How much will the cat weigh after 3 weeks?

c. Write an equation that represents the relationship between the weight of the cat in pounds and weeks on the special diet.

Answer 1

Part C:

W(t) = 5.75 + 0.25*t <-- the cat weights 5.75 pounds and gains 1/4=0.25 pounds per week

For 8 pounds,

8 = 5.75 + 0.25t

2.25 = 0.25t

225 = 25t

t=9

9 weeks to get to 8 pounds

For 11 pounds,

11 = 5.75 + 0.25t

5.25 = 0.25t

525 = 25t

t =21

21 weeks to get to 11 pounds

After 3 weeks, W(3) = 5.75 + 3*0.25 = 5.75 + 0.75 = 6.5 pounds