# Find the equation of the family of curves

**Question description**

1. Find the equation of the family of curves dy/dx=2x^-2 that passes through the point (-1,3).

a.y=1-2/x

b.y=1-2x

c.y=2x-1

d.y=3x-2

2. Given dy/dx=3/2x^1/2+3x and x>_ 0, find the equation of the family of curves which pass through the point (1,0).

a. f(x)=3/2x^2-x^3/2+5/2

b. f(x)=3/2x^2+x^3-5/2

c. f(x)=3x^2+x^3/2-4

d. f(x)=3/2x^2+x^3/2-5/2

3. Given dy/dx=3x^2/x^3+5 find the equation of the family of curves that pass through the point (0,0)

a. f(x)=In (x^3+5)-1

b. f(x)=In (x^3+5)-In (5)

c. f(x)=In (x^3+5)+In (5)

d. f(x)=In X^3-5

4. The balance in an account triples in 20 years. assuming that interest is compounded continuously, what is the annual percentage rate?

a. 4.48

b. 5.49

c. 6.67

d. 3.47

5. A certain type of bacteria increases continuously at a rate proportional to the number present. If there are 500 present at a given time and 1,000 present 2 hours later, how many hours (from the initial time) will it take for the numbers to be 2,500? Round answer 2 decimal places.

a. 3.54

b. 4.29

c. 4.64

d. 5.02

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