Rate of Change Worksheets Grade 8

1. A rocket's altitude during launch is modeled by the equation h(t) = 3.2 × 10^4 + 8.5 × 10^3t, where h is altitude in meters and t is time in seconds after launch. What was the rocket's initial altitude at the moment of launch?
2. Max is reading a book for a school project. The book has 338 pages, and Max reads 15 pages each day. If Max reads at a constant rate, what is the rate of change (pages per day) and the initial value (pages read before starting, which is 0)?
3. A scientist is studying bacterial growth in a lab. The initial population is 200 bacteria, and the population doubles every 3 hours. Write an exponential function in the form y = a(b)^x that models the bacterial population, where x is the number of hours and y is the total population.

…and 5 more problems

1. A linear function has a slope of 6 and passes through the point (0, 11). What is the initial value of the function?
2. A scientist is studying bacterial growth in a lab. The initial population is 500 bacteria, and the population doubles every 3 hours. Write an exponential function in the form y = a * b^x that models the bacterial population, where y is the total population and x is the number of 3-hour periods that have passed.
3. Noah is filling a pool with water. The pool already has 40 gallons of water in it. A hose adds 18 gallons of water each minute. If the pool fills at a constant rate, what is the rate of change (gallons per minute) and the initial value (starting amount of water)?

…and 5 more problems

1. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A second triangle is created by applying the transformation (x, y) → (2x, 2y) to all vertices of the first triangle. What is the area of the larger triangle?
2. (2.5 × 10⁶) × (4.0 × 10⁻³) = ?
3. (4.2 × 10⁵) × (2.5 × 10³) = ?

…and 6 more problems