Active EOC Math 1 Review

Which expression is equivalent to $$x^9y^2\cdot\left(x^3\right)^6\cdot\left(y^4\right)^8?$$

What is the x-intercept of a line that has a y-intercept of 5 and slope 5?

(Hint: y=mx+b and y=0)

What is the average rate of change of hte function $$y=5\left(\frac{1}{4}\right)^x$$ over the interval [-1,5]?

At the beginning of an experiment, there are 50 bacteria in a certain culture. If the number of bacteria doubles every hour, how many bacteria will be in the culture at the end of 7 hours?

The population of a city is increasing 4% every five years. In 1960, the population of this city was 1500 people. What will be the population of this city in 2025?

What is the smallest positive integer such that the value of $$f\left(x\right)=-3x^2+8x$$ exceeds the value of $$g\left(x\right)=-7x+10$$ ?

The population growth for a species of birds, in thousands, can be represented by the function $$p\left(t\right)=40\left(1.15\right)^t$$ , where t is the number of years since 2004. What is the approximate average rate of change of the population between the years 2007 and 2011?

A company's profit is described by the equation $$P\left(x\right)=-5x^2+200x+1000$$ , where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?

What is the y-intercept of the line that passes through the points (2, 0) and (-2, 12)?

What is the equation that generates the sequence below?

1, 4, 7, 10, 13, ...