Solve the following:

a) 2^{2x}-2(2^{x})=3

b) a bacterial culture starts with 1500 bacteria. After 5h, the estimated count is 35 000. What is the doubling period?

c) When the function f(x)=ax^{3}+7x^{2}+bx-8 is divided by (x+1) it has a remainder of 18; and (x-2) is a factor. Determine a and b.