Algebra Word Problem Solutions

${\displaystyle \frac{4}{3}=\left(\frac{2}{15}\right)j}$

How do exponential functions differ from polynomial and rational functions?

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. [T] The Gompertz equation has been used to model tumor growth in the human body. Starting from one tumor cell on day 1 and assuming α=0.1α=0.1 and a carrying capacity of 10 million cells, how long does it take to reach “detection” stage at 5 million cells?

Find a recursive rule that models the exponential decay of ${\displaystyle y=1600{\left(0.97\right)}^t}$

Biff observes that in every math test he has taken this year, he has scored 2 points higher than the previous test. His score on the first test was 56. He models his test scores with the exponential function ${\displaystyle s\left(n\right)=28\cdot 2^n}$ where s(n) is the score on his nth test. Is this a reasonable model? Explain.

Determine the slope of the line represented by the linear equation 5x+6y=40
1.5
2.6
3.${\displaystyle \frac{5}{6}}$
4.${\displaystyle \frac{-5}{6}}$

Rewrite as an exponential equation
${\displaystyle \ln 5=y}$

Graph the rational functions. $y=\frac{x}{(x^2)-2}$

Find three decimals that make the number sentence true. 1.75>____

Determine which type of function-linear, quadratic, or exponential-would be best for modeling each situation below. You do not need to write an equation for the situation. a. Bailey is growing bacteria on a petri dish for science class. The population of bacteria doubles every 20 minutes, so the initial number of bacteria is 1000, then 2000, then 4000, then 8000, etc. b. Avery is working on her math homework. She finished nine problems in class. She knows that, on average, she can do three problems in five minutes. c. Keiton loves catapults. He is building a small catapult that will launch an apple into the air and over the fence into his friend 's backyard.

Tell whether the function represents exponential growth or exponential decay. Explain.
${\displaystyle y=\left(\frac{1}{2}\right){\left(1.01\right)}^x}$

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: $P(x)=a(x-\alpha )(x-\beta )(x-\gamma ),a\ne 0$
Type 2: Two real zeros, one repeated: $P(x)=a(x-\alpha )2(x-\beta ),a\ne 0$
Type 3: One real zero repeated three times: $P(x)=a(x-\alpha )3,a\ne 0$

Type 4: One real and two imaginary zeros: $P(x)=(x-\alpha )(ax2+bx+c),\mathrm{△}=b2-4ac<0,a\ne 0$
Experiment with the graphs of Type 4 cubics. What is the geometrical significance of $\alpha \alpha$ and the quadratic factor which has imaginary zeros?

Find the solution of the initial-value problem. $y^{″}+81y=0,y(0)=1,y^{\prime }(0)=-1$

Contain linear equations with constants in denominators. Solve each equation. ${\displaystyle \frac{x}{5}=(\frac{x}{6}+1)}$

${\displaystyle (1+2i)²(1-2i)²}$

Use the graphs of f and g to graph
h(x) = (f + g)(x). (Graph segments with closed endpoints.)

In the following equation/s, find the indefinite integral :-
$\int \frac{x^2}{x-1}dx$

For each polynomial, state the constant term, the leading coefficient, and the degree of the polynomial.
$5x^2-8x+2x^4-3$

Solve the given equation using linear differential equations.
$y^{\prime }=\csc x+y\cot x$

Solve for x and y.
3x+12y=-30...(1)
6x+6y=-24...(2)