Find the equation of the family of curves

timer Asked: Mar 3rd, 2013

Question Description

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