
Solving
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}+bx8 is divided by (x+1) it has a remainder of 18; and (x2) is a factor. Determine a and b.

Re: Solving
(a) let $\displaystyle u = 2^x$ ... can you solve $\displaystyle u^2  2u = 3$ ?
(b) $\displaystyle y = y_0 e^{kt}$
$\displaystyle 35000 = 1500e^{k \cdot 5}$
solve for the growth constant $\displaystyle k$, then determine the time $\displaystyle t$ when $\displaystyle y = 3000$
(c) $\displaystyle f(1) = 18$ and $\displaystyle f(2) = 0$ ... why?
you should get two equations with two unknowns ... solve for a and b