Master Algebra 1 Word Problems with our Comprehensive Practice

${\displaystyle d\frac{P}{dt}=kP(1-\frac{P}{M})(1-\frac{m}{P}))}$
$\frac{dP}{dt}=kP(1-\frac{P}{M})(1-\frac{m}{P})$

Solve this differential equation using separation of variables. Only separate the equations and integration (not solving for P)
M= carrying capacity (maximum value)
m= threshold value (minimum value)
k= the proportionality constant

Determine the first six terms of the sequence defined by each of these recurrence relations and initial conditions.
a) $a_n=(a_n-1)2,a_1=2$ ( Just find its general formula )

Solve over the interval

$$\begin{gathered} [0,2\pi ) \\ 2(co{s}^2)x+cosx=0 \end{gathered}$$

State whether the equation represents exponential growth, exponential decay, or neither. $y={0.9}^x$

The factored form of a quadratic function is $f(x)=(x‒p)(x‒q)$. The standard form of a quadratic function is ${\displaystyle f\left(x\right)=a{x}^2+bx+c}$. The factored form for a quadratic function tells us the x-intercepts of the quadratic function, while the standard form for a quadratic function tells us the y-intercept of the quadratic function.
Answer the following question:
If $p=2$ and $q=-3$, use what you have learned about multiplying polynomials to
- write the factored form of the quadratic function f(x)
- write the standard form for the quadratic function f(x)

Determine the absolute value of the complex number $z=5+12i$