Worksheet 5.1 - Separable Differential Equations With Answers

Worksheet 5.1 - Separable Differential Equations With Answers - Calculus Maximus Page 2

Calculus Maximus

WS 5.1: Separable Diff EQ

5. (’93-AB42) (Calculator permitted) A puppy weighs 2.0 pounds and birth and 3.5 pounds two months

later. If the weight of the puppy during the first 6 months is increasing at a rate proportional to its

weight, then how much will the puppy weigh when it is 3 months old?

(A) 4.2 pounds

(B) 4.6 pounds

(D) 5.6 pounds

(E) 6.5 pounds

6. (’98-AB84) (Calculator permitted) Population y grows according to the equation

= ky , where k is

a constant and t is measured in years. If the population doubles every 10 years, then the value of k is

(A) 0.069

(B) 0.200

(D) 3.322

(E) 5.000

7. (’93-BC38) (Calculator Permitted) During a certain epidemic, the number of people that are infected

at any time increases at a rate proportional to the number of people that are infected at that time. If

1,000 people are infected when the epidemic is first discovered, and 1,200 are infected 7 days later,

how many people are infected 12 days after the epidemic is first discovered?

(A) 343

(B) 1,343

(D) 1,400

(E) 2,057

= 2 y and if y = 1 when

t = 0

, what is the value of t for which y =

8. (’85-BC33) If

ln 2

(A)

(B)

(C)

(D)

(E)

ln 2

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Worksheet 5.1 - Separable Differential Equations With Answers - Calculus Maximus Page 2