SAT Math: Advanced Math

The profit of a company is modeled by the equation $P = R - C$, where $P$ is the profit, $R$ is the revenue, and $C$ is the cost. If the revenue $R$ is given by $R = 5x^2 + 10x$ and the cost $C$ is given by $C = 2x^2 + 5x + 100$, where $x$ is the number of units sold, which quadratic equation represents the profit?

A farmer wants to enclose a rectangular field with 400 meters of fencing. One side of the field is along a river and does not need fencing. If the area of the field is 2000 square meters, find the dimensions of the field.

A ball is thrown upward from a height of 4 feet with an initial velocity of 32 feet per second. The height $h$ of the ball after $t$ seconds is given by $h = -16t^2 + 32t + 4$. At what time will the ball hit the ground?

Identify the initial value and growth factor in the exponential equation $P(t) = 250(1.08)^t$, where $P(t)$ represents the population after $t$ years.

A town's population starts at 1500 and grows at a rate of 3% per year. Which exponential equation models this population growth?

A radioactive substance has a half-life of 20 years. If the initial amount is 100 grams, how much will remain after 60 years?

Solve the quadratic equation $x^2 + 4x - 6 = 0$.

A bacteria population doubles every 4 hours. If the initial population is 50, what will the population be after 12 hours?

An investment of $2000 earns compound interest at a rate of 5% per year. What will be the value of the investment after 10 years?

A rectangular garden has a width of $x$ meters. The length is 5 meters more than the width. If the area of the garden is 36 square meters, which of the following equation represents the area of the garden?